In early January 2024, I wrote an answer to reader-of-the-blog Vince’s question about his retirement portfolio. A quick summary of that article is:
If Vince’s portfolio is $4.2M and his annual spending needs are $100,000, he’ll be entering retirement following (essentially) a “2.38% Rule.” That’s way more conservative than the classic 4% Rule.
He doesn’t need to expose himself to undo risk. 60% stocks, 55% stocks, 50% stocks…Vince will be successful in any of these portfolios. Since he has “won the game” of career financial success, he can “stop playing the game” by taking some of his chips off the table a.k.a. reducing his exposure to risk assets (stocks).
Vince wrote back! He asked this week:
If the market goes down, should I perform my annual rebalance into stocks, or because we have 20 years of spending in our fixed income portion of our portfolio, should we only rebalance into bonds from now on when our equities get too high. It may come back to living comfortably vs. passing on more money to heirs. (I choose the former).
Vince
Ahh! Rebalancing. Let’s dive in.
Two Sentences on Rebalancing
Rebalancing is the act of adjusting the asset allocation within an investment portfolio (how much in stocks? how much in bonds? etc.) to maintain the desired level of risk and return.
To learn more, here’s a deep dive on the topic of rebalancing.
Vince’s Question, Summarized
This is such an interesting question!
Vince is asking:
Should Vince’s rebalancing go in both directions?
If stocks are up compared to bonds, should Vince sell stocks to buy more bonds?
If stocks are down compared to bonds, should he sell bonds to buy more stocks?
Why does it matter? Because part of Vince’s portfolio approach is that his bond allocation represents 20 years’ worth of spending in his portfolio. He’s not measuring in percentages! He’s measuring in years’ worth of spending.
So, in essence, Vince is asking: should he rebalance, even if doing so results in him having “fewer years of bonds” than he’s comfortable with?
We need to understand two different schools of thought regarding portfolio construction. These two schools are definitely similar but with slight, nuanced differences.
The first is the “bottoms-up, bucket method” described on the blog before. It recommends an investor assign a timeline to every dollar in their portfolio, then align those timelines with appropriate levels of risk in investment assets. The money with a 6-month timeline needs to be in cash or ultra low-risk Treasury notes. The money with a 30-year timeline should be in higher risk assets (like stocks) in search of greater returns.
The other common approach is the “expected risk, expected return” method. This approach uses historical data and the investor’s unique risk appetite (a combination of their age, their cashflow needs, their unique mental approach to losing money, etc.) to hone in on the “right” allocation for them. Younger, riskier investors can stomach more stocks, while older, risk-averse investors should own more bonds, etc.
Ideally, the portfolio’s future “expected returns” are then used to test the validity of the overall financial plan (e.g. via Monte Carlo simulation).
Which Method is “Right?”
Which method is right?
Both methods work. And, in theory, both should lead to very similar outcomes. The two methods differ more in mindset than in “brass tacks.”
I prefer the “bottoms-up, bucket method” because it puts planning first (“give the dollar a job and a timeline”) and then determines appropriate investments. I used that approach in my original response to Vince. He is also using that method in his new question today. Vince feels particularly safe with 20 years’ worth of spending in fixed income. Those dollars have timelines, and he’s built an appropriate cash, CD, and bond ladder for those timelines.
Is It Right to Rebalance?
Should Vince rebalance? Let’s start by using some reasonable numbers to add color to Vince’s question.
Let’s say Vince needs $100,000 per year from his portfolio. And, based on his personal risk tolerance, he wants 20 years of that annual spending in bonds**. Easy math. That’s $2 million in bonds.
**For what it’s worth, most of the time for most investors, their timelines beyond 10 years should not be in bonds. The math simply says otherwise – that money should be in a higher risk asset, like stocks.
But finance is personal. And many retirees are acutely aware of the fact that “this is all the money I have!” Extra caution – aka extra fixed income – is understandable. It’s helps the investor sleep at night…return on sleeplessness!!! And as long as that extra fixed income doesn’t damage the portfolio’s probability of success, I’m ok with it.
Ok. $2 million in bonds, meaning the rest of Vince’s $4.3M portfolio (as of this writing) is in stocks. That’s $2.3M in stocks. That’s a 55% stock, 45% bond allocation.
Looks like a 55/45 split, no?
Next, we need hypothetical returns.
Let’s say over the rest of 2024, bonds provide their expected 5% interest while stocks drop 8%. But Vince withdraws $100,000 (from bonds, because that’s why they’re there) to support his annual expenditures. Vince’s portfolio will shift to $2.1M in stocks, $2.0M in bonds.
That’s a 51% stock, 49% bond portfolio. Should Vince rebalance to 55% / 45%?! Let’s go back to first principles. Why did Vince end up 55/45 in the first place?
Because he wanted 20 years of bonds to cover his next 20 years of expenses, and everything thereafter went to stocks. And because his financial plan appears to be perfectly successful with that portfolio.
We should look through that exact same lens when considering rebalancing.
Does Vince still need 20 years of bonds to sleep at night? Or, with one more year in the rearview mirror, is he comfortable with 19 years of bonds? This is a mental/personal question.
Depending on that answer, does Vince need more/fewer bonds than he has right now?
And finally, does his financial plan’s probability of success change depending on his rebalancing? This is a math/brass tacks question.
Based on Vince’s investing rationale, his rebalancing decision is a function of bond prices.“I said I needed ~20 years of bonds to sleep at night; do I have them?”
The stock portion of his portfolio has little to do with that! If stocks go up 30%, but he still has 20 years of bonds, I don’t think he should rebalance into even more bonds.
Off the Balance Beam
As asset prices move, our portfolio allocations shift like desert sand beneath our feet. Our targeted risk and return can veer off course and our financial plan’s likelihood of success can decay. These are reasons to rebalance.
However, rebalancing isn’t always needed, depending on your portfolio and the unique rationale of your financial plan. As in Vince’s case, some market movements create more rebalancing needs than others.
Thank you for reading! If you enjoyed this article, join 8000+ subscribers who read my 2-minute weekly email, where I send you links to the smartest financial content I find online every week.
-Jesse
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Options trading offers a complex yet potentially rewarding approach to the stock market, allowing investors to buy or sell assets at predetermined prices within specific time frames. Unlike direct stock purchases, these contracts grant the right without obligating the transaction, providing a strategic tool for managing investment risks and capitalizing on market predictions.
This guide will explore the fundamentals of options trading, including the differences between call and put options, the process of getting approved for trading, and strategies for minimizing risks while maximizing returns.
What is an option?
An option is a contract that grants you the option buyer, the right, but not the obligation, to buy or sell a particular asset at a set price on a particular date or within a select window of time.
It’s also classified as a derivative, with the associated value directly linked to the underlying asset. This price point is also known as the strike or exercise price, and the expiration date specifies when the contract terminates.
But how does this benefit investors? Well, it’s a cost-efficient way to manage risk because you’re only investing in the opportunity to purchase shares at another date, and not the stock itself. Options also allow you to sell your existing shares at a set price if the market tanks to limit your losses.
How does options trading work?
However, it’s a bit more complex than simply buying and selling shares. In essence, options traders are taking a gamble on the direction they think the stock price will go in. That way, they won’t have to buy or short the actual stock when they think the market is going to skyrocket or dip.
Furthermore, there’s a relatively extensive process to get approved as an options trader. You’ll also need to open a brokerage account and maintain a set amount of reserves to remain in good standing as an investor.
And should you decide not to exercise the option, you’re free to walk away with no strings attached. You can also rake in a little more cash by selling the option, or options contract, to an investor who’s interested.
Benefits of Trading Options
There are several benefits to trading options, including:
Flexibility: Options can be used to hedge against potential losses in other investments, or to generate income through the writing of options.
Leverage: Because options allow traders to control a large amount of underlying assets for a relatively small investment, they offer significant leverage.
Limited risk: The potential loss on an options trade is limited to the premium paid for the option.
Customization: Options can be customized to meet the specific needs and objectives of the trader.
Liquidity: Options are traded on organized exchanges, making it easy to buy and sell them.
Versatility: Options can be used in a variety of market conditions, including bearish, bullish, and neutral markets.
Types of Options
Still sold on the idea of trading options? There are two types to choose from:
Call Options: these are deposit rights to purchase the stock at a later date. If the call option is not exercised before the expiration date, you lose your investment in the option and the right to purchase the underlying stock at the strike price.
Put Options: these are premiums paid to hedge against the risk of a market downturn. They are similar to an insurance policy that protects your investment. If the price of the underlying stock plummets, you will still have your right to sell a set number of shares at the exercise price. But if the market stays intact or swings upward and you decide not to sell, your premium is lost.
You should also know that call and put holders are owners of options contracts. They absorb minimal risk as there’s no obligation to buy or sell, regardless of market performance. Instead, they are free to exercise the option when they see fit.
By contrast, call and put writers are sellers of options contracts. Unfortunately, they’re exposed to more risk because they must follow through on their promise to buy or sell if the holder exercises their option.
Options Pricing
Options pricing refers to the process of determining the value of an options contract. There are several factors that can impact the price of an options contract. These include the underlying asset’s price, the option’s strike price, the time remaining until the option’s expiration date, the option’s implied volatility, and the risk-free interest rate.
One of the most widely used methods for calculating the price of an option is the Black-Scholes model. This model takes into account the aforementioned factors to determine the theoretical value of an options contract. Other methods for pricing options include the binomial model and the Monte Carlo simulation.
Keep in mind that the price of an options contract can fluctuate significantly over time, and may be affected by a variety of market conditions. Therefore, options traders should carefully consider the potential risks and rewards of their trades and use appropriate risk management strategies.
Risks and Rewards of Options Trading
Options trading can be a complex and risky endeavor, but it can also provide the opportunity for significant profits. It’s essential for investors to understand the potential risks and rewards involved to make informed decisions and manage risk effectively.
One way to minimize risk when trading options is to use investment strategies like spreading. This involves buying and selling options at different strike prices and expiration dates to offset potential losses.
Another investment strategy is to use stop-loss orders. They allow you to set a certain price at which your trade will be automatically closed to prevent further losses.
Additionally, you should diversify your portfolio and not rely too heavily on options trading. That way, if one trade doesn’t work out, you won’t be left with all your eggs in one basket.
Investors can maximize their profits and minimize risks by understanding options trading and implementing risk management strategies.
Getting Started with Options Trading
Getting started with options trading requires more than a simple phone call to a broker or an online purchase. It demands a proactive approach and thoughtful preparation to set the stage for your trading activities.
Step 1: Select a Brokerage Firm
Like it or not, you’ll have to work with a brokerage firm to get screened and cleared to trade options. But don’t just settle for the first broker you find. Shop around and carefully analyze your options before making a decision. Remember, they’ll be evaluating your experience, so you should do the same.
Do a little research to determine if they’ll be a good fit. Pay attention to consumer reviews, services they offer, costs or commissions structure, account minimums, and educational resources they offer, just to name a few.
Furthermore, inquire about educational resources, including self-guided online courses and webinars, along with telephone, virtual, and live support designed to help you identify and understand the most strategic routes when trading options.
Finally, feel free to ask questions as they arise to ensure you have all the information you need to make a well-informed decision. The more access you have to support staff, the better.
Remember, it’s your hard-earned money that will be used to buy options, so you want to make sure you derive the greatest benefit in exchange for your investment.
Step 2: Get Screened
Once you’ve selected a brokerage firm, the next step is to get screened. This is a prerequisite to being assigned a trading level. Before screening can begin, the broker will want to get an understanding of your investment goals and which types of options you’re most interested in. They will also inquire about your trading experience and will request additional information about your finances.
Your information will be compiled by the broker and analyzed to determine the optimal trading level. Levels range from 1 to 5 and will dictate the types of transactions you’re able to engage in.
Furthermore, you’ll need to maintain a minimum balance of $2,000 in your account at all times, per industry requirements. Additionally, purchasing a call option may mandate a margin account or line of credit to serve as security. Check with the brokerage firm to confirm minimum reserves and additional details regarding margin accounts.
Step 3: Start Trading Options
Now that you’re in the clear, you have to use your knowledge and judgment to make some critical choices that can boost or dent your wallet. Some important considerations:
How you think the stock will perform – Anticipating an increase in price? A call option is best as it allows you to turn a profit if the price surpasses the strike price within the window of time allotted by the option, and. In this case, you will be in the money. But if the market price drops below the strike price, you’ll be out of the money.
By contrast, if you already own shares and are expecting a dip in the price, you would purchase a put option. You’ll be in the money if the market price drops below the strike price, and out of the money if the market price ends up exceeding the strike price.
The length of the option – Stock options are only valid for a set period of time. Some options last for several days or months, while others span several years.
Optimal strike price – It’s difficult to determine where the stock price will end up, so you’ll have to make an educated guess regarding the strike price before purchasing an option.
Thinking the price of a share currently trading for $50 will increase to $75? Let’s assume you purchase a call option with a strike price below $75. (You want a call option that leaves a little wiggle room to account for the cost of the option). If the share price exceeds the strike price, you will be in the money or turn a profit.
Now assume you owned these shares and expected the share price to drop to $25? By purchasing a put option with a strike price that is above $25 and accounts for the cost of the option, you’ll be in the money if the price does drop below this point.
Bottom Line
Options trading is a sophisticated tool for seasoned investors, offering strategic depth to portfolio management. However, it’s not the sole method to mitigate risk or seek returns. Stock trading presents a more accessible alternative, with its direct approach and fewer entry barriers.
While options can leverage market movements and offer protection, they demand a solid grasp of market intricacies. In contrast, stock trading provides a straightforward path to investment growth. Choosing between them depends on your risk tolerance, investment goals, and willingness to explore market complexities.
The internet has done wonders in the world of Investment Tracking. With websites like Mint and now Power Wallet, tracking your finances for free online is a snap. But one thing that’s been missing is a robust tool to automatically track your investments.
Best Investment Tracking App
Sites like Mint do allow you to link your investment accounts. But they don’t help you understand your asset allocation or investing expenses in any meaningful way. And that brings me to a site I’ve recently starting using called Empower.
Empower is the best investment tracking tool that I’ve ever used. It solves several problems for me:
It automatically links to my investment accounts, keeping my holdings updated throughout the trading day;
It tracks the fees I’m paying for each mutual fund and ETF I own;
It provides detailed asset allocation data for my investments, much like the X-Ray feature of Morningstar;
It alerts me when my asset allocation is over or under-weighted as compared to a target asset allocation model determined based on my age and tolerance for risk; and
It offers retirement income calculations and projections based on your investments, projected social security, pensions, annuities, and other retirement income sources.
I’ve enjoyed the tool so much, that I thought a detailed review was in order.
Getting Started
Empower is a free tool. To get started, you simply create an account with your email address and password. Once you have access to the site, you can connect just about all of your bank and investment accounts into Empower.
I had no trouble connecting accounts from Citi, Capital One 360, Scottrade and Fidelity. And once all of your accounts are connected, the fun begins.
The Dashboard
The Dashboard is the one place you’ll find high level information about all your finances. While I use Empower primarily for my investments, you can also track your checking and savings accounts. In fact, they offer what is called a Cash Manager that lets you see all of your spending in one place.
Investment Tracking
Empower does a great job of tracking investments real-time. And just as importantly, the layout of the site and the way in which information about your investments is displayed is the best I’ve seen (note, the image is not of my personal investments):
What you can’t see from the above screen shot is what happens as you roll the cursor over parts of the screen. On the graph at the top left, you’ll see your investment balance by date. And as you roll the cursor over the colored ring top right, you’ll see details about each of your investment accounts.
And what’s really cool is when you click on an individual account in the list at the bottom. As you can see from the screenshot above, the graph highlights the portion of your total attributed to that account, and the colored ring breaks out the portion of the circle related to the selected account.
Now the truth is that while the above is really cool, it’s just information. It doesn’t really give you any analysis that you can actually use. But the next few features do.
Mutual Fund and ETF Expenses
As I’ve said many times, keeping investment expenses low is one of the most important factors for successful investing. And Empower gives you two tools to help you. The first is a breakdown of your investment costs by mutual fund or ETF.
In my case, total investment costs are a real eye-opener. Empower breaks down the cost by fund or ETF, so that you can focus your analysis and determine whether you need to make any changes. Through using the tool, it became clear to me that there are a couple of funds I need to dump for less expensive alternatives.
Cryptocurrency
Empower now offers the ability to track your cryptocurrency within the dashboard. Since last year, Empower saw its users increase the value of linked accounts by about 28% – so they’ve decided to start including the ability to track crypto now, too.
Since more people are starting to invest in things like Bitcoin, it only makes sense that you’d be able to track your tokens. Currently, you have the ability to track thousands of tokens across hundreds of different cryptocurrency exchanges. This is, of course, in addition to the loads of other benefits you’ll get from Empower.
401(k) Fee Analyzer
The second tool to help fight the high cost of investing is revolutionary. It’s called the 401k Fee Analyzer.
The first time you run this tool, it will base its analysis on data not specific to your retirement funds. But you can get additional data on 401k expenses from your employer or broker to get more accurate results.
What’s so great about the analyzer is that it doesn’t stop with just the expense ratios of the funds and ETFs you own. That part’s easy. It also looks at the costs funds charge you for trading, which aren’t reflected in the expense ratio. And it looks at administrative costs charged to run the 401k, which are often passed down to employees.
If you have a 401k, this tool by itself makes it worth checking out Empower. And it’s a good reminder as to why most folks should transfer their 401k to a rollover IRA when they leave their employer.
Asset Allocation Tools
The next handy tool is its asset allocation feature. The first thing it does is breaks down all of your investments by their asset class. And if a single fund or ETF contains investments that span more than one asset class, as most do, Empower slices and dices the fund to apportion your account into each relevant asset class.
You can click on each investment in the box chart at the top or the list at the bottom to get details of your asset classes. This is extremely helpful when it comes to rebalancing your portfolio.
Investment Checkup
With the click of a button Empower will analyze your investments. It compares your actual asset allocation with your target allocation, and flags asset classes in which you are over or under-weighted. It’s an easy way to see if you need to rebalance.
Note that in the above screenshot heading is a reference to my “target allocation.” You can set this by entering your name, how many years to retirement, and your investing style (e.g., aggressive, conservative). It takes all of 10 seconds, and Empower then generates a target allocation for you.
Robust Retirement Calculator
Finally, Empower offers a free retirement calculator. The tool takes into account your current investments, age, projected social security, projected savings, and just about any other information you want to include. Using monte carlo analysis, it then determines whether you are on track to retire.
As you can see from the screenshot, the retirement planner displays the results in easy to understand graphs. It also makes change the assumptions (e.g., inflation, social security) very easy.
So what’s not to like?
Frankly, not much. One thing I haven’t mentioned is that an advisor is available for a call or a live chat. When you log into your account, you’ll see a picture of your advisor, his or her name, and telephone number. And even better, they don’t hound you. I’ve not heard from my advisor, and that’s how I want it. If I need to speak to him, I’ll give him a call. But it’s good to know that’s an option.
Empower also has mobile versions of its site for iPhone, iPad and Android. I use the iPad app and have had no issues. I’ve not had any issues with linking accounts. Occasionally I have to provide or confirm my login credentials for certain accounts. But that’s it.
But there are three things that could be improved:
You can’t enter your own target asset allocation model. Empower creates one for you based on your age, time to retirement, and investing style. This is probably fine for the majority of investors, but a custom option would be nice.
The daily updates on stock and bond prices is a bit slow. As compared to Wikinvest, another tool I’ve used before, Empower could be faster
It does not include the cost basis of your investments, which would be nice.
So there you have it. Its an excellent tool. If you want to give it a try, visit the Empower website.
Check It Out: Empower Review
Learn More: The Best Stock Tracking Apps
Empower Personal Wealth, LLC (“EPW”) compensates Webpals Systems S. C LTD for new leads. Webpals Systems S. C LTD is not an investment client of Personal Capital Advisors Corporation or Empower Advisory Group, LLC
Rob Berger is the founder of Dough Roller and the Dough Roller Money Podcast. A former securities law attorney and Forbes deputy editor, Rob is the author of the book Retire Before Mom and Dad. He educates independent investors on his YouTube channel and at RobBerger.com.
The Heston model is an options pricing model developed to address some of the shortcomings in the Black-Scholes model when pricing European options. In contrast to the Black-Scholes model, the Heston model uses stochastic, not constant, volatility as a key variable to determine option prices.
Developed by mathematician Steve Heston in 1993, this model is thought to be more real-world in nature since implied volatility percentages change during an option’s life. However, the Heston model is just one of many option valuation techniques to consider.
What Is the Heston Model?
The Heston model is used to gauge the value of options. The main difference between this and other models is how volatility is treated. The Heston model for option pricing assumes that volatility is stochastic, or random. That simply means that volatility is treated as a variable, in contrast to other models that assume constant or local volatility.
Option prices are made up of several variables — often referred to as the Greeks. It is important to understand price inputs in order to know how to trade options. Volatility is a major piece of the price of an option. The higher the implied volatility, the more valuable the option is. The Heston approach accounts for this by assuming there is a relationship between a stock’s price and its volatility.
💡 Quick Tip: In order to profit from purchasing a stock, the price has to rise. But an options trading account offers more flexibility, and an options trader might gain if the price rises or falls. This is a high-risk strategy, and investors can lose money if the trade moves in the wrong direction.
How Does the Heston Model Work?
By assuming that volatility is random, many traders believe the Heston option pricing model works better than the Black-Scholes model since it captures the true nature of volatility. The Heston approach is considered a superior model to the Black-Scholes, too. The downside is that it can be more complicated to calculate. Moreover, it can only be used on European options — those that can be exercised only at expiration.
Like other option pricing models, the Heston method attempts to determine the time value piece of an option’s total value. Intrinsic value is straightforward to figure out since it is just the difference between the stock price and strike price. Intrinsic value and time value comprise an option’s total worth.
Heston Model Pros and Cons
The Heston option pricing model has several advantages and disadvantages. By incorporating variable volatility characteristics, an options trader can have more confidence in the Heston model’s output reflecting observed market behavior versus other valuation techniques. The Heston model achieves increased accuracy by considering correlations between the price of a stock and its volatility. It also assumes that volatility exhibits mean reversion.
Additionally, Heston’s approach yields a closed-form solution that can simplify what is a complex mathematical equation.
The Heston model has its limitations. For one thing, the output is only as good as the variables you assume. This model is also thought to be ill-equipped to price options close to expiration due to instances when implied volatility might be extremely high.
Perhaps the biggest downside is its complexity versus Black Scholes and the binomial options pricing model.
Pros
Cons
Incorporates more realistic market conditions such as changing volatility levels
Only useful on European-style options
Prices options considering the price and maturity variables on volatility
Only as good as the inputs used
Yields a closed-form solution that can be used to compare an option’s value to its market price
Considered not an accurate gauge to price short-term options with high volatility
Heston vs Black-Scholes Model
Understanding the differences between the Heston model and the Black-Scholes model can help you determine which might work best when you trade options.
Heston Model
Black-Scholes Model
Assumes that volatility is random
Assumes that volatility is constant
Incorporates a relationship between a stock’s price and its volatility
Does not incorporate correlations between a stock’s price and volatility
Can be used in a variety of market conditions
Prices options under one set of volatility parameters
Finally, user-friendly options trading is here.*
Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.
Heston Model Formula Explained
The Heston volatility model includes several mathematical inputs. Knowing these can help you find the right strategies for trading options. Understanding the model inside and out can arm you with the quantitative armor other traders might not possess.
Here is the full Heston model formula:
Where:
• St = specific asset price at time t
• r = the risk-free interest rate, often a short-term Treasury rate
• √Vt = volatility (standard deviation) of the asset
• σ = volatility of volatility
• θ = long-run price variance
• k = reversion rate to the long-term price variance
• dt = indefinitely small positive time increment
• W1t = Brownian motion of the asset price
• W2t = Brownian motion of the asset’s price variance
Note that the two Brownian motions are negatively correlated. For example, a drop in the asset price will see an increase in volatility. The two Brownians are related by the following equation:
Where ρ is the correlation.
In his original paper describing this model, Heston provided default parameters for the equations above which include:
• St = 100
• r = 0
• Vt = 0.01
• σ = 0.1
• θ = 0.01
• k = 2
• ρ = 0
• Option maturity = 0.5 year
Further calibration of the model requires advanced mathematical analysis.
Other Option Pricing Models
The Heston option pricing is just one of many approaches to consider. Let’s outline several of the most common methods you might use to price options.
Binomial Model
The binomial model uses an iterative approach using several periods to value American-style options. It follows a binomial pricing tree, which can be useful in illustrating how option prices change from one period to another. This method is considered intuitive and is used more often than Black-Sholes.
Risk-Neutral Probability
The risk-neutral approach to option pricing assumes that risk is not considered. This method can help a trader assess the true value of an option outside of market risk conditions.
Monte Carlo Simulation
Monte Carlo simulations are sometimes used to gauge the value of options. This method utilizes computer simulations to create thousands of potential outcomes. Option values can be calculated based on the probability-weighted computer output.
Monte Carlo simulation is used to generate realistic market conditions which can be useful for options traders as they attempt to assess how an option value will fluctuate over time. However, it can be time-consuming and costly to run these complex programmatic scenarios.
The Takeaway
The Heston model prices options using stochastic (random) volatility to more accurately model options pricing behavior. The more well-known Black-Scholes option pricing model assumes that implied volatility remains constant.
Some traders believe that the Heston model approach works better to incorporate practical, real-world conditions. Still, there are many techniques to price options for you to consider when you trade.
Qualified investors who are ready to try their hand at options trading, despite the risks involved, might consider checking out SoFi’s options trading platform. The platform’s user-friendly design allows investors to trade through the mobile app or web platform, and get important metrics like breakeven percentage, maximum profit/loss, and more with the click of a button.
Plus, SoFi offers educational resources — including a step-by-step in-app guide — to help you learn more about options trading. Trading options involves high-risk strategies, and should be undertaken by experienced investors.
With SoFi, user-friendly options trading is finally here.
FAQ
What is the Heston model used for?
The Heston Model is used for pricing European options. It uses stochastic volatility to arrive at pricing outcomes, helping traders value options. If a trader determines that an option is over- or under-valued, they might sell or buy the option, then hold it through expiration or trade out of the position before expiration. It is important to remember that European options, unlike American options, cannot be exercised early.
Is the Heston model better than Black-Scholes?
It’s hard to conclude that the Heston stochastic volatility model is better than the more widely known Black-Scholes model. In contrast to Black-Scholes, the Heston model assumes that volatility can change. The Heston model can be more useful to traders since it assumes implied volatility, an important variable for options pricing, increases as options become more in-the-money or out-of-the-money. While the Heston model is considered to be more accurate, it comes with increased computational complexity or in layman’s terms…it’s slower.
What does stochastic local volatility mean?
Local volatility is a basic application of the Black-Scholes model. It accounts for the requirement to price-in skewness into option values. Stochastic volatility contrasts local volatility in that the former can produce a more real-world forward volatility profile. It’s thought that stochastic volatility can overprice options while local volatility and the Black-Scholes method might underprice options.
Photo credit: iStock/FG Trade
SoFi Invest® The information provided is not meant to provide investment or financial advice. Also, past performance is no guarantee of future results. Investment decisions should be based on an individual’s specific financial needs, goals, and risk profile. SoFi can’t guarantee future financial performance. Advisory services offered through SoFi Wealth, LLC. SoFi Securities, LLC, member FINRA / SIPC . SoFi Invest refers to the three investment and trading platforms operated by Social Finance, Inc. and its affiliates (described below). Individual customer accounts may be subject to the terms applicable to one or more of the platforms below. 1) Automated Investing—The Automated Investing platform is owned by SoFi Wealth LLC, an SEC registered investment advisor (“Sofi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC, an affiliated SEC registered broker dealer and member FINRA/SIPC, (“Sofi Securities).
2) Active Investing—The Active Investing platform is owned by SoFi Securities LLC. Clearing and custody of all securities are provided by APEX Clearing Corporation.
3) Cryptocurrency is offered by SoFi Digital Assets, LLC, a FinCEN registered Money Service Business.
For additional disclosures related to the SoFi Invest platforms described above, including state licensure of Sofi Digital Assets, LLC, please visit www.sofi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform. Information related to lending products contained herein should not be construed as an offer or prequalification for any loan product offered by SoFi Bank, N.A.
Options involve risks, including substantial risk of loss and the possibility an investor may lose the entire amount invested in a short period of time. Before an investor begins trading options they should familiarize themselves with the Characteristics and Risks of Standardized Options . Tax considerations with options transactions are unique, investors should consult with their tax advisor to understand the impact to their taxes. SOIN0322020
The Heston model is an options pricing model developed to address some of the shortcomings in the Black-Scholes model when pricing European options. In contrast to the Black-Scholes model, the Heston model uses stochastic, not constant, volatility as a key variable to determine option prices.
Developed by mathematician Steve Heston in 1993, this model is thought to be more real-world in nature since implied volatility percentages change during an option’s life. However, the Heston model is just one of many option valuation techniques to consider.
What Is the Heston Model?
The Heston model is used to gauge the value of options. The main difference between this and other models is how volatility is treated. The Heston model for option pricing assumes that volatility is stochastic, or random. That simply means that volatility is treated as a variable, in contrast to other models that assume constant or local volatility.
Option prices are made up of several variables — often referred to as the Greeks. It is important to understand price inputs in order to know how to trade options. Volatility is a major piece of the price of an option. The higher the implied volatility, the more valuable the option is. The Heston approach accounts for this by assuming there is a relationship between a stock’s price and its volatility.
💡 Quick Tip: In order to profit from purchasing a stock, the price has to rise. But an options trading account offers more flexibility, and an options trader might gain if the price rises or falls. This is a high-risk strategy, and investors can lose money if the trade moves in the wrong direction.
How Does the Heston Model Work?
By assuming that volatility is random, many traders believe the Heston option pricing model works better than the Black-Scholes model since it captures the true nature of volatility. The Heston approach is considered a superior model to the Black-Scholes, too. The downside is that it can be more complicated to calculate. Moreover, it can only be used on European options — those that can be exercised only at expiration.
Like other option pricing models, the Heston method attempts to determine the time value piece of an option’s total value. Intrinsic value is straightforward to figure out since it is just the difference between the stock price and strike price. Intrinsic value and time value comprise an option’s total worth.
Heston Model Pros and Cons
The Heston option pricing model has several advantages and disadvantages. By incorporating variable volatility characteristics, an options trader can have more confidence in the Heston model’s output reflecting observed market behavior versus other valuation techniques. The Heston model achieves increased accuracy by considering correlations between the price of a stock and its volatility. It also assumes that volatility exhibits mean reversion.
Additionally, Heston’s approach yields a closed-form solution that can simplify what is a complex mathematical equation.
The Heston model has its limitations. For one thing, the output is only as good as the variables you assume. This model is also thought to be ill-equipped to price options close to expiration due to instances when implied volatility might be extremely high.
Perhaps the biggest downside is its complexity versus Black Scholes and the binomial options pricing model.
Pros
Cons
Incorporates more realistic market conditions such as changing volatility levels
Only useful on European-style options
Prices options considering the price and maturity variables on volatility
Only as good as the inputs used
Yields a closed-form solution that can be used to compare an option’s value to its market price
Considered not an accurate gauge to price short-term options with high volatility
Heston vs Black-Scholes Model
Understanding the differences between the Heston model and the Black-Scholes model can help you determine which might work best when you trade options.
Heston Model
Black-Scholes Model
Assumes that volatility is random
Assumes that volatility is constant
Incorporates a relationship between a stock’s price and its volatility
Does not incorporate correlations between a stock’s price and volatility
Can be used in a variety of market conditions
Prices options under one set of volatility parameters
Finally, user-friendly options trading is here.*
Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.
Heston Model Formula Explained
The Heston volatility model includes several mathematical inputs. Knowing these can help you find the right strategies for trading options. Understanding the model inside and out can arm you with the quantitative armor other traders might not possess.
Here is the full Heston model formula:
Where:
• St = specific asset price at time t
• r = the risk-free interest rate, often a short-term Treasury rate
• √Vt = volatility (standard deviation) of the asset
• σ = volatility of volatility
• θ = long-run price variance
• k = reversion rate to the long-term price variance
• dt = indefinitely small positive time increment
• W1t = Brownian motion of the asset price
• W2t = Brownian motion of the asset’s price variance
Note that the two Brownian motions are negatively correlated. For example, a drop in the asset price will see an increase in volatility. The two Brownians are related by the following equation:
Where ρ is the correlation.
In his original paper describing this model, Heston provided default parameters for the equations above which include:
• St = 100
• r = 0
• Vt = 0.01
• σ = 0.1
• θ = 0.01
• k = 2
• ρ = 0
• Option maturity = 0.5 year
Further calibration of the model requires advanced mathematical analysis.
Other Option Pricing Models
The Heston option pricing is just one of many approaches to consider. Let’s outline several of the most common methods you might use to price options.
Binomial Model
The binomial model uses an iterative approach using several periods to value American-style options. It follows a binomial pricing tree, which can be useful in illustrating how option prices change from one period to another. This method is considered intuitive and is used more often than Black-Sholes.
Risk-Neutral Probability
The risk-neutral approach to option pricing assumes that risk is not considered. This method can help a trader assess the true value of an option outside of market risk conditions.
Monte Carlo Simulation
Monte Carlo simulations are sometimes used to gauge the value of options. This method utilizes computer simulations to create thousands of potential outcomes. Option values can be calculated based on the probability-weighted computer output.
Monte Carlo simulation is used to generate realistic market conditions which can be useful for options traders as they attempt to assess how an option value will fluctuate over time. However, it can be time-consuming and costly to run these complex programmatic scenarios.
The Takeaway
The Heston model prices options using stochastic (random) volatility to more accurately model options pricing behavior. The more well-known Black-Scholes option pricing model assumes that implied volatility remains constant.
Some traders believe that the Heston model approach works better to incorporate practical, real-world conditions. Still, there are many techniques to price options for you to consider when you trade.
Qualified investors who are ready to try their hand at options trading, despite the risks involved, might consider checking out SoFi’s options trading platform. The platform’s user-friendly design allows investors to trade through the mobile app or web platform, and get important metrics like breakeven percentage, maximum profit/loss, and more with the click of a button.
Plus, SoFi offers educational resources — including a step-by-step in-app guide — to help you learn more about options trading. Trading options involves high-risk strategies, and should be undertaken by experienced investors.
With SoFi, user-friendly options trading is finally here.
FAQ
What is the Heston model used for?
The Heston Model is used for pricing European options. It uses stochastic volatility to arrive at pricing outcomes, helping traders value options. If a trader determines that an option is over- or under-valued, they might sell or buy the option, then hold it through expiration or trade out of the position before expiration. It is important to remember that European options, unlike American options, cannot be exercised early.
Is the Heston model better than Black-Scholes?
It’s hard to conclude that the Heston stochastic volatility model is better than the more widely known Black-Scholes model. In contrast to Black-Scholes, the Heston model assumes that volatility can change. The Heston model can be more useful to traders since it assumes implied volatility, an important variable for options pricing, increases as options become more in-the-money or out-of-the-money. While the Heston model is considered to be more accurate, it comes with increased computational complexity or in layman’s terms…it’s slower.
What does stochastic local volatility mean?
Local volatility is a basic application of the Black-Scholes model. It accounts for the requirement to price-in skewness into option values. Stochastic volatility contrasts local volatility in that the former can produce a more real-world forward volatility profile. It’s thought that stochastic volatility can overprice options while local volatility and the Black-Scholes method might underprice options.
Photo credit: iStock/FG Trade
SoFi Invest® The information provided is not meant to provide investment or financial advice. Also, past performance is no guarantee of future results. Investment decisions should be based on an individual’s specific financial needs, goals, and risk profile. SoFi can’t guarantee future financial performance. Advisory services offered through SoFi Wealth, LLC. SoFi Securities, LLC, member FINRA / SIPC . SoFi Invest refers to the three investment and trading platforms operated by Social Finance, Inc. and its affiliates (described below). Individual customer accounts may be subject to the terms applicable to one or more of the platforms below. 1) Automated Investing—The Automated Investing platform is owned by SoFi Wealth LLC, an SEC registered investment advisor (“Sofi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC, an affiliated SEC registered broker dealer and member FINRA/SIPC, (“Sofi Securities).
2) Active Investing—The Active Investing platform is owned by SoFi Securities LLC. Clearing and custody of all securities are provided by APEX Clearing Corporation.
3) Cryptocurrency is offered by SoFi Digital Assets, LLC, a FinCEN registered Money Service Business.
For additional disclosures related to the SoFi Invest platforms described above, including state licensure of Sofi Digital Assets, LLC, please visit www.sofi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform. Information related to lending products contained herein should not be construed as an offer or prequalification for any loan product offered by SoFi Bank, N.A.
Options involve risks, including substantial risk of loss and the possibility an investor may lose the entire amount invested in a short period of time. Before an investor begins trading options they should familiarize themselves with the Characteristics and Risks of Standardized Options . Tax considerations with options transactions are unique, investors should consult with their tax advisor to understand the impact to their taxes. SOIN0322020
You don’t have to search all that hard to find the best Italy cruises — most leading cruise lines offer dozens of itineraries that visit Italian ports, often in conjunction with neighboring countries France, Greece and Croatia.
The reason? Italy has it all: coastlines on both the Mediterranean and the Adriatic, historic port cities (Rome, Venice and Naples among them) and spectacular islands (including Sicily, Sardinia, Capri and Elba).
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Plus, with a cruise season that runs from early April through late October (and even year-round for a few cruise lines), Italy offers something for everyone. Travel here to find an alluring mix of impeccably preserved historic sites, renowned regional cuisines and natural wonders waiting to be discovered.
Here are eight of the best Italy cruises for every type of traveler.
Best Italy cruises for cultural immersion: Azamara
Azamara pioneered the concept of single-country itineraries, which allow for greater cultural immersion and even overnight stays in select ports. The cruise line’s 11-night voyage in October 2024 is one of its most comprehensive.
The sailing begins in Monte Carlo, Monaco, and ends in Rome (Civitavecchia), with visits to seven more Italian ports and Tunis, Tunisia. You’ll explore Genoa, Livorno (overnight for Florence/Pisa), Porto Santo Stefano (on the Tuscan coast), Cagliari (on Sardinia), Trapani (on Sicily), Amalfi and Sorrento.
This voyage is aboard the 684-passenger Azamara Onward, one of the cruise line’s four virtually identical ships. (All are former Renaissance R-class ships built in the early 2000s and renovated over the past several years.) The vessels’ intimate size and Azamara’s focus on cultural experiences and shore excursions emphasizing history and food (including cooking classes and market tours) make for an immersive cruise itinerary.
Other Italy-Intensive voyages in 2023 and 2024 include the following: a 10-night voyage in October 2023 aboard Azamara Quest, a 10-night voyage in April 2024 aboard Azamara Pursuit, and a seven-night voyage in May 2024 aboard Azamara Quest.
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Best Italy cruises for small-ship lovers: Windstar Cruises
WINDSTAR CRUISES
It’s rare to find a cruise itinerary so fully focused on one specific region of Italy, but Windstar Cruises’ small ships — three classic sailing yachts and three all-suite motor yachts, which accommodate 148 to 342 guests — allow it to offer cruises to less-frequented ports.
Windstar’s 10-day Sicilian Splendors, aboard its 342-passenger sailing yacht Wind Surf, is available on multiple dates in 2023, 2024 and 2025. The ship will cruise round-trip from Rome and call on six Italian ports: Catania (for Mount Etna), Porto Empedocle (for the ancient ruins at Agrigento) and Trapani (for its signature colored salts and Marsala wines), all in Sicily; the island of Lipari (the largest of seven Aeolian Islands); and Sorrento and Amalfi on the stunning Amalfi Coast. The cruise also visits the neighboring islands of Malta and Gozo.
Five-masted Wind Surf is the world’s largest sailing ship. It manages to be intimate without feeling claustrophobic, although it is worth noting that none of its staterooms or suites has a balcony. There is, however, ample deck space for relaxation, with a pool and two hot tubs, as well as inviting alfresco bars and dining areas.
Related: The 2 classes of Windstar ships, explained
Indoors, the ship’s restaurants and social spaces, such as the Veranda Restaurant, Stella Bistro and the Compass Rose Bar, are light-filled, with elegant neutral decor refreshed in 2019.
Musical entertainment takes place in the Wind Surf Lounge and Compass Rose Bar, and Windstar’s excellent dining program reflects an ongoing partnership with the James Beard Foundation. In select tender ports, passengers can enjoy a watersports platform and take out sea kayaks and stand-up paddleboards.
Best Italy cruises for onboard pampering: Ritz-Carlton Yacht Collection
EMILIA WRONSKI/THE POINTS GUY
If enjoying yacht-style indulgence as you explore Southern Italy is on your cruise wish list, consider the Ritz-Carlton Yacht Collection’s 10-night Rome to Valletta itinerary in May 2024. This cruise visits scenic hot spots such as Sorrento and Amalfi on the Amalfi Coast, history-rich Siracusa in Sicily and three ports (Gallipoli, Taranto and Otranto) in lesser-known Puglia, located on the heel of boot-shaped Italy, before passengers disembark in Malta.
Ritz-Carlton, which entered the cruise realm in 2021 with its 298-passenger luxury yacht, Evrima, offers an all-inclusive “yachting lifestyle” experience. This leisurely sailing features overnights in Sorrento and Taranto and two sea days with ample ways to enjoy onboard pampering. The ship’s spacious suites are designed with a contemporary residential feel and range in size from 300 square feet with an 81-square-foot terrace to 1,091 square feet with a 635-square-foot terrace.
Evrima also offers nine bars and dining venues featuring menus created to reflect the ports visited. For culinary indulgence, guests can book a table at S.E.A., a specialty dining experience designed by Chef Sven Elverfeld of Aqua, the Michelin three-starred restaurant at The Ritz-Carlton in Wolfsburg, Germany.
The ship also features chicly designed spaces for relaxing and socializing, such as the Pool House lounge overlooking an aft infinity pool, a second pool located next to the alfresco restaurant Mistral, a panoramic Observation Lounge and a full-service Ritz-Carlton Spa.
Related: The best luxury cruise lines for elegance and exclusivity
Best Italy cruises for foodies: Silversea Cruises
Barbara Muckermann and Adam Sachs during the event “Celebrating the Harvest” organized by Pasta Mancini in Monte San Pietrangeli, Italy. SILVERSEA CRUISES
The three newest ships in the Silversea Cruises fleet — Silver Moon, Silver Dawn and 2023’s first-in-class Silver Nova — all feature the cruise line’s immersive culinary program known as S.A.L.T. (Sea and Land Taste). When Silversea’s next ship, the 728-passenger Silver Ray, debuts in 2024, it will also take its guests on culinary-focused journeys — among them an 11-day Rome to Venice itinerary in June 2024.
The itinerary includes calls on seven ports in Italy: Rome, Naples, Sorrento, Palermo, Siracusa, Trieste and Venice. The sailing also visits ports in Malta, Montenegro and Croatia.
Silversea’s sailings blend food-centric excursions — such as a visit to a family farm for a tasting of fresh cheese, salami and olive oil in Sorrento — with the onboard S.A.L.T. program to make sampling local cuisine a natural part of the cruise experience. The day-to-day menus at S.A.L.T. Kitchen are all inspired by the ports visited. The Terrain menu focuses on that day’s port while the Voyage menu draws from the best flavors of the entire itinerary.
Passengers aboard Silver Ray should definitely pack an appetite — in addition to S.A.L.T. Kitchen, the ship features seven other restaurants. They are La Dame for haute French cuisine, Atlantide for signature fine dining (think caviar and lobster), Kaiseki for Japanese sushi and teppanyaki (as well as pan-Asian dishes), Silver Note for tapas-style dining and live music, The Grill for casual burgers and salads, La Terrazza for handmade pasta and other Italian specialties, and Spaccanapoli for thin-crusted Naples-style pizza. With 11 nights aboard, there’s time to sample all of them.
Related: The ultimate guide to cruise ship food and dining
Best Italy cruises for families: Norwegian Cruise Line
NORWEGIAN CRUISE LINE
If an Italy adventure with the entire family sounds like the perfect cruise vacation in 2024, Norwegian Cruise Line’s new Norwegian Viva, launching in August 2023 as the sister ship to 2022’s Norwegian Prima, is an ideal playground for guests of all ages.
The most Italy-focused itinerary? The 10-day Mediterranean: Italy, Greece & Croatia cruise (offered aboard 3,099-guest Viva in late June and late September 2024) calls on six ports in Italy — Rome, Livorno, Naples, Messina, Siracusa and Trieste — as well as the islands of Corfu and Malta; Koper, Slovenia; and Dubrovnik and Split in Croatia.
This itinerary is rich in history and culture, including the ancient landmarks of Rome, the archeological wonders of Pompeii and the Leaning Tower of Pisa near Livorno, plus the beauty and culinary treats (sweet cannoli and savory arancini) of Sicily, where Viva makes two port calls. Though the cruise ends in Trieste, the wonders of Venice are just 90 minutes away, so adding a few extra nights to explore its colorful, canal-laced islands is a must.
Onboard Viva, you’ll enjoy more than a dozen dining options (five of them complimentary, including the casual and family-friendly Indulge Food Hall), 16 bars and lounges and all the fun activities/entertainment (including a production of the Broadway hit “Beetlejuice: The Musical”) that the line offers.
Related: Best cruise lines for families
Top amenities include the three-deck Viva Speedway for exhilarating go-kart racing, three thrilling slides (two of them 10-story corkscrew dry slides and one tidal-wave-style waterslide), virtual-reality gaming in the Galaxy Pavilion, tech-enhanced minigolf and more. Also, Viva’s generous outside deck space — especially Deck 8’s Ocean Boulevard with its lively Indulge Outdoor Lounge and sleek Infinity Beach pools — is ideal for scenic cruising in the Mediterranean and Adriatic.
Best Italy cruises for couples: Oceania Cruises
OCEANIA VISTA. ERICA SILVERSTEIN/THE POINTS GUY
The sophisticated onboard ambiance and a romantic itinerary are a lovely combination, and couples can enjoy both on the 12-night Mediterranean Tapestry sailing offered in June 2024 aboard Oceania Cruises’ newest vessel, Oceania Vista.
The 1,200-passenger ship, which debuted in May 2023, will visit four top ports in Italy — Venice/Trieste in Northern Italy, Taormina in Sicily, Amalfi/Positano in Southern Italy and Civitavecchia for a day in Rome.
Beyond Italy, this itinerary offers a sampling of scenic locales in six other Adriatic and Mediterranean countries with a possible pre-cruise stay in Venice. You’ll visit Korcula and Split in Croatia; Kotor, Montenegro; Igoumanitsa and Katakolon in Greece; Ajaccio, Corsica; Monte Carlo, Monaco; Marseille, France; and Barcelona, Spain.
Oceania caters to couples seeking an upscale cruise experience with a culinary focus. Onboard Vista, the atmosphere is sleek and polished, with interior decor awash in elegant neutrals of varying patterns and textures, all woven together into a soothing mosaic (in some cases, literally, as tiled vignettes are used throughout the ship). Vista’s bars and lounges, especially the Martini Bar and the Grand Lounge, are so chic you’ll want to get dressed up every night to enjoy one of the craft cocktails on their newly enhanced menus.
All specialty dining is included in the cruise fare, and stand-out meals at Polo Grill (for an excellent steakhouse menu), Toscana (for authentic Italian, including recipes by Vista’s godmother Giada De Laurentiis) and Red Ginger (for flavorful pan-Asian) are just a reservation away. Two new eateries, Aquamar Kitchen and Ember, serve wellness-focused cuisine and casual American comfort food, respectively, and an expanded Culinary Arts Center lets guests who love to cook take hands-on classes.
Best of all, Vista is an all-balcony ship, so every stateroom features access to fresh air (French Veranda Staterooms don’t have an outdoor sitting area, however). Veranda Staterooms and Concierge Level Veranda Staterooms offer a spacious 290 square feet of indoor space — and some of the best standard bathrooms at sea with roomy walk-in showers and ample storage.
Related: The best cruises for couples seeking romance and together time at sea
Best Italy cruises for travelers on a budget: Royal Caribbean
ROYAL CARIBBEAN
To score a budget cruise fare in the Mediterranean, it helps to look for sailings aboard a cruise line’s older ships. If Italy is your main focus for a future cruise, it’s hard to beat the seven-night Western Mediterranean itinerary in September 2024 aboard Royal Caribbean’s Voyager of the Seas.
It visits five Italian ports: Venice/Ravenna, Messina in Sicily, Naples, Rome and Livorno (for Florence and Pisa). The ship also calls on Marseille and Barcelona. Voyager’s Italy-focused cruise is a jam-packed itinerary with just one sea day.
Ideal for both couples and multi-generational families, the 3,600-passenger Voyager of the Seas (which debuted in 1999 and was last refurbished in 2019) features seven restaurants (including three complimentary dining venues and specialty restaurant favorites Chops Grille and Giovanni’s Table) and eight bars/lounges.
The ship has been “amped-up” so guests can enjoy features found on Royal Caribbean’s newer ships: Perfect Storm waterslides, FlowRider simulated surfing, Battle for Planet Z laser tag, Voyager Dunes minigolf, Studio B ice-skating shows and reimagined spaces for kids and teens.
Nights aboard Voyager of the Seas will be filled with complimentary entertainment options: production shows in the Royal Theater, pub performances by guest entertainers and bands, game-show competitions, pool parties, outdoor movie nights and a ‘70s disco party.
Best Italy cruises for adults-only ambiance: Viking
Aerial view of the Viking Sea leaving Dubrovnik, Croatia. WHITE RAIN/VIKING CRUISE LINE
Is Venice at the top of your wish list? Does an adults-only cruise on a ship with serene, Scandinavian-inspired interior decor and complimentary wine or beer with lunch and dinner sound ideal?
If so, check out Viking’s 15-night Italy, the Adriatic and Greece itinerary, which sails from Athens to Rome and visits six Italian ports — Venice/Chioggia, Bari, Crotone, Messina, Naples and Rome — with three days spent in Venice. As a bonus, you’ll also visit ports in Greece (Katakolon and Corfu), Croatia (Dubrovnik, Split and Sibenik) and Montenegro (Kotor).
Offered on multiple dates in fall 2023, 2024 and 2025, this itinerary is chock full of port experiences; there are no sea days, and a total of 13 cities are visited. Viking includes one free guided shore excursion in each port, usually a panoramic bus tour or historic walking tour. Use that as an overview and then explore on your own or book one of the cruise line’s longer or more specialized excursions. Onboard guest speakers also offer insight into the ports visited and the cultural landscape.
The cruise line’s nine ocean ships are all identical and accommodate 930 passengers, most of whom are couples over age 55. Onboard dining is available in eight restaurants, including the main venue, The Restaurant and the buffet-style World Cafe, the casual Pool Grill and the Norwegian-focused Mamsen’s. Guests can also reserve dinner at two specialty restaurants (at no extra charge): Manfredi’s for Italian cuisine and The Chef’s Table for multi-course, wine-paired menus that rotate throughout the cruise.
Afternoon tea is served in the elegant Wintergarden. The Aquavit Terrace overlooking the aft infinity pool is a sunny spot to enjoy alfresco dining.
If you’re willing to come back early from port, Viking’s ocean ships offer plenty of ways to relax on board. All passengers enjoy complimentary access to the ship’s thermal suite in the LivNordic Spa. It features a thalassotherapy pool, steam room, sauna and snow room. The Main Pool has a retractable roof and can be enjoyed no matter what the weather. However, if you want to live it up at night, note that the ship does not have an onboard casino.
Bottom line
The best Italy cruises offer access to some of the country’s most-loved cities, as well as a chance to explore some of its sunny islands and lesser-known coastal ports. No matter the itinerary, you’re guaranteed to enjoy the splendid landscapes, treasured antiquities and, of course, the incredible gelato.
I’m generally an even-keeled guy. I don’t get worked up about much. I understand that different people have different perspectives, so I try to be respectful when others disagree with me. Having said that, there are indeed certain things that piss me off. Here are a couple that are centered around the idea of planning your retirement based on how much of your paycheck you should save.
Myth #1: You Need to Have 70% of Your Income
For instance, I get mad-dog lathered up at traditional advice about how much to save for retirement, such as this article at Business Insider (echoed here at The Wall Street Journal):
So how much are you supposed to be saving in order to finance 20 to 30 years post-work? The commonly accepted rule of thumb is that you’ll want about 70% of your former annual income â at least â to continue living at or near the style to which you’ve been accustomed.
A Monte Carlo simulation is a mathematical technique used by investors and others to estimate the probability of different outcomes given a situation where multiple variables may come into play. Monte Carlo simulations are used in such a wide range of industries â e.g., physics, engineering, meteorology, finance, and more â that the term doesnât […]
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