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Aug

2023

The Heston Model: Defined & Explained with Calculations

By Mike Zaccardi, CMT, CFA | Growing Wealth, invest, Investing | Comments Off

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.

*Check out the OCC Options Disclosure Document.

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:

• S_t = specific asset price at time t

• r = the risk-free interest rate, often a short-term Treasury rate

• √V_t = 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

• W_1t = Brownian motion of the asset price

• W_2t = 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:

• S_t = 100

• r = 0

• V_t = 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.

Investors who are ready to try their hand at options trading despite the risks involved, might consider checking out SoFi’s options trading platform offered through SoFi Securities, LLC. The platform’s user-friendly design allows investors to buy put and call options 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. Currently, investors can not sell options on SoFi Active Invest®.

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®

INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE

SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
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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.

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.
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Aug

2023

Guide to Barrier Options

By Mike Zaccardi, CMT, CFA | Growing Wealth, invest, Investing | Comments Off

Barrier options are complex derivative products that have payoffs based on whether an underlying asset crosses a pre-specified price threshold.

There are several types of barrier options, and they are used to hedge a portfolio or simply to speculate on an underlying asset’s price change, much like regular call and put options. But due to the restriction of the barrier, premiums tend to be lower when initiating the trade.

What Is a Barrier Option?

Barrier options are just like regular options with the inclusion of an additional barrier to the regular option payoff.

Beginners start trading options with purchases of simple puts and calls. Options trading quickly turns complex as you dive into writing options, combination strategies, and exotic options.

In contrast to barrier options, plain-vanilla options typically have some value as the asset approaches and then crosses the strike price. Before an option is in the money, the value is known as time or extrinsic value.

Once an option is in the money, the option price is a combination of intrinsic value and extrinsic value.

A barrier option’s payoff (or lack thereof) is predicated by the underlying asset crossing some barrier price determined upon option initiation. Once the barrier is crossed, the nature of the option changes.

In some cases, the option is “normal” but after crossing the barrier it becomes worthless forever, simply by crossing the barrier. Other barrier options begin as worthless (or close to it), but revert to a normal option once they cross the barrier, even if they later cross the barrier again.

These products can be used to develop simple or complex strategies in options trading.

💡 Quick Tip: If you’re an experienced investor and bullish about a stock, purchasing call options (rather than the stock itself) can allow you to take the same position, with less cash outlay. It is possible to lose money trading options, if the price moves against you.

How Barrier Options Work

First, recognize that a barrier option is an exotic option — it comes with added rules and features compared to the more common American-style and European-style flavors. A barrier option is also path-dependent, much like non-exotic options, in that its value is determined by changes in the underlying asset’s market price.

A key feature of a barrier option is when it can be exercised. Depending on the barrier option pricing terms, its value activates or becomes worthless at that crossover price.

Pros and Cons of Barrier Options

Barrier options work like puts and calls, but they feature more restrictions than standard American or European options. That leads to advantages and disadvantages for both the holder and seller of a barrier option.

Barrier options’ pricing terms often dictate how and when traders of these derivatives might use them in their trading strategies.

In general, there is less risk for the barrier option seller and more restrictions put on the owner. Both parties, however, should be aware that there is less liquidity in barrier option markets compared to more actively traded standard options markets.

Pros	Cons
Lower option premiums means a cheaper way to trade for option buyers	Less chance to exercise due to restrictive terms (for the holder)
Reduced risk to the option writer	Poor liquidity versus plain vanilla puts and calls
Can be more customized than standard options	Added complexity makes barrier options tougher to understand for new traders

Finally, user-friendly options trading is here.^*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

*Check out the OCC Options Disclosure Document.

Knock-In and Knock-Out Barrier Options

Knock-in and knock-out barrier options are the two common types of barrier options. Knock-in options are unable to be exercised until the underlying security crosses a trigger point, deemed the barrier price.

Knock-out options can be exercised immediately, but they turn inactive (worthless) at the time of breaching the barrier price. It can be helpful to see how these products work via barrier options examples.

Knock-In

Knock-In Option Example

Let’s say you buy a knock-in barrier call option featuring a strike price of $100 and a barrier of $110 while the underlying security trades at $90. The option is not exercisable until the underlying asset’s price climbs above the $110 barrier.

The option owner pays a premium but that premium is lower than for a regular call. Why?

Two reasons:

1. The barrier option won’t be immediately exercisable and is worth close to zero until the underlying asset crosses the barrier price.

2. The barrier price typically exceeds the strike price for calls and is below the strike price for puts. That means the likelihood to have any intrinsic value is lower because the option must first breach the barrier. A regular option has intrinsic value once it exceeds the strike price.

However, after the barrier is breached the barrier option will trade like any other standard call option with a strike of $100, no matter what the price does subsequent to breaching the barrier. If the barrier is not broken, the seller keeps the premium.

Knock-in barrier options are broken down further into up-and-in or down-and-in options.

The call above is an up-and-in barrier option example, the asset price must move up for the option to be exercisable. Down-and-in means the price must move down to the barrier before it is exercisable and typically is used for barrier put options.

Knock-Out

Knock-Out Option Example

For a knock-out barrier option, we’ll assume you bought an up-and-out call option with a barrier of $50 and a strike of $40 while the underlying asset trades at $35. If the asset rallies to $50, the option will cease to exist and be worth nothing.

A knock-out option is worthless even if the underlying asset’s price touches the barrier price for only a moment before falling back.

The call above is immediately exercisable and will always trade at a lower price than a regular call. Why?

Reasons include:

1. If the underlying asset is far from the barrier, the option will be cheaper than a regular option as it is still at some small risk of breaching the barrier and being worthless.

2. As the underlying asset moves closer to the barrier the option will move towards zero as the risk of crossing the barrier increases dramatically.

Knock-out barrier options are broken down further into up-and-out or down-and-out options. The difference is which way the price must move to breach the barrier and become worthless.

As you can see, barrier options pricing puts a spin on the usual calls and puts you might be familiar with.

Types of Barrier Options

Beyond knock-in and knock-out options, there are a few other barrier option types to learn about.

Rebate Barrier Options

Rebate barrier options have provisions that allow the holder to retain some value of the option contract even if the barrier price is not reached. It might be a percentage of the premium paid from the execution of the trade.

This might be seen as a less risky version of barrier options as it is not an all-or-nothing approach.

Turbo Warrant Barrier Options

Turbo warrant barrier options are traded more actively in overseas markets. They are a category of down-and-out options and feature high leverage.

While they can be risky, turbo warranty barrier options are also less volatile than other types.

Parisian Option

Both time and price are key variables with Parisian barrier options. They work similarly to Asian options. They are different in that the underlying security’s price must not only cross the barrier but stay above that price for a predetermined time period before the contract is in effect.

The Takeaway

Barrier options offer traders another means to hedge a portfolio or speculate on an underlying asset. This type of option is exotic, meaning it is more complex than plain vanilla puts and calls.

With barrier “in” options, the call or put does not go into effect until a barrier price level is hit while “out” options are active until the barrier price is touched.

Barrier options give investors more flexibility and customization at a cheaper price, but they can be more restrictive and less liquid than other options.

With SoFi, user-friendly options trading is finally here.

FAQ

Are barrier options American or European?

Barrier options are complex exotic options different from the two common styles of options: American and European. While American-style options can be exercised at any time, before and at expiration, and while European-style options can be exercised only at expiration, barrier options are exercisable only after the barrier price is reached.

How are barrier options valued?

Barrier options have a path-dependent value since their worth is based on the underlying asset’s price movements. It is only when the underlying price crosses the barrier price that the option has value and can be exercised. If that predetermined barrier option price is never reached, then the option is worthless with a typical knock-out option. Knock-in options are non-exercisable until they reach the barrier price.

Can you replicate barrier options?

Some strategies can replicate the structure and payoff profile of barrier options. Many of these analyses were performed by academics over recent decades. The goal is often to produce sound portfolio hedging techniques.

Photo credit: iStock/nensuria

SoFi Invest®

INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE

Aug

2023

Married Put Options Strategy: Defined & Explained

By Mike Zaccardi, CMT, CFA | Growing Wealth, invest, Investing | Comments Off

A married put is an options trading strategy wherein an investor purchases an asset and an at-the-money put to protect against a price drop in the shares.

This options strategy works to safeguard the shareholder from sharp declines in the underlying asset price. You can easily calculate your maximum gain, maximum loss, and breakeven with a married put strategy.

What Is a Married Put?

A married put is an options strategy in which you simultaneously buy shares of an asset and purchase an ATM put to protect against a decline in the asset price.

You might execute a married put strategy when you are concerned about a large downward move in the asset price over the short run, but you want to own the asset for a longer timeframe.

Recommended: How to Trade Options

How Does a Married Put Work?

A married put works by protecting the investor from a decrease in the price of an asset. With a married put, you are still exposed to a loss, but losses are limited based on the strike price of the put option purchased.

At the same time, a married put allows you to participate in upside in the underlying shares since the most you can lose with the put option is the premium paid, while your long asset position has unlimited upside.

At the money put options can be expensive insurance. The premium you pay for the downside protection can make the strategy prohibitively expensive. Put option pricing depends on many variables, known as the options Greeks. A married put options strategy can work well with low-volatility stocks if you are worried about upcoming bad news on the company.

Maximum Profit

One of the main advantages of a married put options strategy is that you retain unlimited upside potential since you are long the asset and the most you can lose on the put option is the premium paid.

Maximum profit = unlimited

Breakeven

A married put’s breakeven is a straightforward calculation. It is the price you paid for the asset plus the premium paid to acquire the put option. The asset must rise by more than the amount of the premium for the strategy to exhibit gains.

Breakeven = Cost basis of the asset + premium paid

Recommended: Call vs. Put Options: The Differences

Maximum Loss

This is where the married put strategy really shines. The maximum loss is the cost of the asset minus the put option’s strike price, plus the premium paid. The most you can lose with a married put is limited.

Maximum loss = cost basis of the underlying asset – strike + premium paid

Finally, user-friendly options trading is here.^*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

*Check out the OCC Options Disclosure Document.

Married Put Example

It is helpful to run through a married put example to show the benefits and downsides of this options strategy. This can help when comparing it against other options strategies.

Let’s say you want to own shares on XYZ stock currently priced at $100. You buy 100 shares for a total of $10,000 and an at the money put option contract for $5. Each option contract covers 100 shares, so the total premium is $500.

Your breakeven is $105. That is the per share cost of the stock plus the premium paid. If the stock is unchanged at the expiration of the options contract, you will have a loss of $5 on the strategy.

Your maximum profit is unlimited since the stock has no upside cap. If the stock rallies to $120 by expiration, you have a $15 gain. While the maximum profit is unlimited, it will be lower than if you’d purchased only the shares due to the cost of the put.

Your maximum loss is $5, the put option premium. In this example, your maximum loss occurs at or below a $95 stock price. You can close the trade by selling the stock and selling-to-close the option. Alternatively, you can sell-to-close the put or let it expire and continue to hold the stock.

Note: The calculations above disregard transaction costs, but due to the purchased puts being at the money these costs can add up.

💡 Quick Tip: Options can be a cost-efficient way to place certain trades, because you typically purchase options contracts, not the underlying security. That said, trading options online can be risky, and best done by those who are not entirely new to investing.

Pros and Cons of Married Puts

Pros	Cons
Offers downside protection	The put option’s premium might be prohibitively expensive
Offers upside participation	Commissions could be high on the put option
Works well on low volatility assets when you believe is a near-term risk of a share price decline	Liquidity on the put option could be weak

Married Puts vs Covered Call

Married Puts	Covered Call
Purchase an at the money put and the underlying asset simultaneously	Sell a call on an asset you already own
Long the asset and long a put option	Collect a premium to enhance a portfolio’s yield
Exit the trade by selling shares and selling-to-close the put option	Roll out by buying-to-close and then selling-to-open another call.

Strategies Similar to Married Puts

There are several options trading strategies similar to married puts. Let’s investigate those.

Protective Puts

A protective put strategy is very close to a married put strategy. The difference is that you already own the asset with a protective put trade. With a married put, you simultaneously buy the asset and put.

Long Calls

A married put behaves the same way as a long call. You own the asset with a married put strategy, but a long call position does not entail owning the underlying shares. Long calls differ from naked calls since you buy-to-open a call option contract in a long call strategy while you sell-to-open calls without owning the underlying shares in a naked call play.

Call Backspreads

A call backspread is a bullish options strategy wherein you sell lower-strike calls and a greater number of higher-strike calls at the same expiration on the same asset. A call backspread offers unlimited upside. You would execute this complex options strategy when you are extremely bullish on a volatile asset. Call backspreads are also known as ratio volatility spreads.

The Takeaway

A married put options strategy is when you purchase an at the money put option and shares of the underlying asset simultaneously. It is a way to limit risk when you want to own shares in a company.

With SoFi, user-friendly options trading is finally here.

FAQ

Is a married put the same as a covered put?

A covered put is the opposite of a married put in that you are short the asset and short a put option in a covered put trade. With a married put, however, you buy the put and the asset at the same time.

Is a married put a good strategy?

A married put can be a good strategy if you want insurance on a new asset position. It is a bullish strategy used if you are worried about potential near-term risks in the asset. By owning a protective put, you have downside protection while still being able to participate in asset price appreciation. You have the right to receive dividends and participate in shareholder votes by owning the stock, too. The downside is that you must pay a premium to own the put option.

What is the difference between puts and calls in options trading?

Puts and calls are two option types. Puts give the holder the right but not the obligation to sell shares of an asset at a specific price and at a specified time. Calls give the holder the right but not the obligation to buy shares of an asset at a specified price and time.

Photo credit: iStock/Renata Angerami

SoFi Invest®

INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE

Aug

2023

What the Binomial Option Pricing Model Is & How It Works

By Mike Zaccardi, CMT, CFA | Growing Wealth, invest, Investing | Comments Off

The binomial option pricing model is a valuation tool that predicts the price of an asset for selected future points in time then uses an iterative approach to work backwards to determine the present value of options on that underlying asset.

The binomial option pricing model has the benefit of being relatively easy to implement and provides visibility into the linkages between the underlying asset price and the option prices as the expiration date approaches.

What Is the Binomial Option Pricing Model?

The binomial option pricing model is a widely used option pricing formula. There are multiple versions of the model, depending on what assumptions the trader wishes to make and what types of options are to be priced.

Fundamentally, the model involves a three-step process:

1. Generate the binomial price tree for the underlying asset.

2. Calculate the options values based on the asset prices for each final node.

3. Calculate the option value at each preceding node.

Recommended: How to Trade Options

Assumptions of the Binomial Option Pricing Model

The binomial option pricing model assumes two possible outcomes: an up or down change in the stock price. While it’s simple in a one-period approach, the model can quickly turn complex over multiple time frames. However, constructing the pricing tree illustrates how an asset’s price changes from period to period.

Another advantage is that the binomial option pricing model can be used to value American, European, and Bermuda-style options. There are adjustments needed to use the binomial model based on which options are being priced. For this discussion, we will focus on American options only.

Other assumptions in the model discussed herein include that the underlying asset pays no dividends, the interest rate is constant, there are no transaction costs, there are no taxes, and that the risk-free rate is constant.

It also assumes investors are risk-neutral.

💡 Quick Tip: If you’re an experienced investor and bullish about a stock, buying call options (rather than the stock itself) can allow you to take the same position, with less cash outlay. It is possible to lose money trading options, if the price moves against you.

How Does the Binomial Model Work?

The binomial option tree is used for finding the current value of an option. This value is equal to the present value of the probability-weighted future payoffs.

Binomial Option Pricing Model Calculations

Let’s dive into calculations for calls and puts. In order to understand how these calculations are made it helps to know the basics of options trading strategies.

Call Options

A call option gives the holder the right but not the obligation to purchase a security at a specific price at a specific time. A call option is in the money when the stock price is above the strike price. A binomial tree’s nodes will value an option at the maximum of zero or its calculated value.

Recommended: How Options Are Priced

When the underlying asset moves up in price, the call option’s payoff (C^up) is the maximum of zero and the stock price (S) multiplied by the up factor (u) and reduced by the exercise price (P_x).

call-options-underlying-asset-moves-up-in-price

When the underlying asset moves down in price, the call option’s payoff (C^down) is the maximum of zero and the stock price (S) multiplied by the down factor (d) and reduced by the exercise price (P_x).

call-options-underlying-asset-moves-down-in-price

The binomial model calculates all possible payoffs, based on these calculations. The final outcomes are then discounted back to calculate the present value.

Put Options

Put options give the holder the right but not the obligation to sell a security at a specific price at a specific time. A put option is in the money when the stock price is below the strike price.

When the underlying asset moves up in price, the put option’s payoff (P^up) is the maximum between zero and the exercise price (P_x) minus the stock price (S) multiplied by the up factor (u).

put-options-underlying-asset-moves-up-in-price

When the underlying asset moves down in price, the put option’s payoff (P^down) is the maximum between zero and the exercise price (P_x) minus the stock price (S) multiplied by the down factor (d).

put-options-underlying-asset-moves-down-in-price

Binomial Model Example

Assumptions

XYZ stock is currently trading at $100 and you wish to calculate the value of a call option with a $105 strike price that will expire in two weeks.

You expect that each week the stock may increase by 10% or decrease by 15%. The risk-free rate is currently 5% and you will be looking for cash settlement rather than delivery of shares. Additionally, XYZ is not expected to pay dividends over the two-week holding period.

You want to view how the option price will move weekly up until expiration and calculate the option value today.

Generate the Binomial Tree

We construct the binomial tree for the prices of XYZ stock.

binomial-tree-step-1-price-tree-generation

At the end of one week (1/52 of a year or 0.02 years) the stock will be priced at either $110 or $85.

After two weeks, (0.04 years) the price will increase to $121 if the price moves up twice in a row. The stock price will be $93.50 if the price moves up then down, or down then up. Finally, if the stock moves down twice in a row the stock will drop to $72.25.

Note that we can create a binomial tree for any time period size and include many more steps at the cost of greater complexity in the calculations.

Calculate Final Option Values

Having forecast the stock price two weeks into the future we can calculate the value of the $105 strike price call option at that time.

The call option will only have value if the stock moves up twice in a row. At that time the shares will be worth $121 and the option will be worth $16.

Stock price – Strike price = $121 – $105 = $16

Work Backward to Calculate Present Values

Before we can perform the present value calculations we need to determine the probability that the stock price, and the call option price, will move along the upward path in the binomial tree during each week.

Fortunately we have all the information we need to calculate the probability based on our initial assumptions. The probability for an up move is:

Where:

• t = the time period in years (1 week = 0.02 years)

• r = the risk-free rate (5%)

• u = up factor ($110 / $100 = 1.1)

• D = down factor ($85 / $100 = 0.85)

Substituting into the equation:

Because there are only two paths at each node the the probability of a down move is:

Given the probabilities and the potential option values at the end of week two, we use the present value calculation to determine the option value for the end of week one.

We repeat this process until we arrive at the value of the call option today.

binomial-tree-step-3-work-backward-to-calculate-present-values

At each step we weigh the final values by their respective probabilities and discount by the risk-free rate using the following equation:

Finally, we arrive at the present value of the call option of $5.82.

Finally, user-friendly options trading is here.^*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

*Check out the OCC Options Disclosure Document.

Pros and Cons of the Binomial Model

Pros	Cons
Simple to calculate	Difficult to predict future prices and probabilities
Can be used on American options	Assumes conditions that are not seen in real-world markets
Can be used over multiple periods	Complexity grows as more periods are considered

Binomial Option Pricing Model vs Black-Scholes Model

The Black-Scholes model comes to a deterministic result based on the inputs. Its inputs are option variables such as the strike price, the current stock price, the time to expiration, the risk-free rate, and the volatility. While the binomial model is considered path dependent, the Black-Scholes model is path independent.

Widely used in practice and considered accurate, the Black-Scholes model makes assumptions that sometimes arrive at options prices that are different from those seen in the real world.

The Black-Scholes model is considered the standard when valuing European options since the model does not allow for options to be exercised early.

Binomial Option Pricing Model	Black-Scholes Model
Probabilistic approach	Deterministic approach
Path dependent with two possible outcomes at each node	Usually accurate, but output prices sometimes deviate from those seen in the real world
Helpful for American options	Helpful for European options

Binomial Option Pricing Model vs Monte Carlo Model

The Monte Carlo model runs thousands of computer simulations to arrive at a solution. Monte Carlo simulation often includes an array of possible paths — some that show higher ending prices and others that show lower prices.

The computer simulations are only as good as the assumptions used. Analysts can tailor the inputs. Often, historical data is used in Monte Carlo simulations which may lead to results that aren’t applicable.

Binomial Option Pricing Model	Monte Carlo Model
An iterative approach that is path dependent	Based on computer simulations
Less computer intensive	You can tailor the inputs and scenarios
Uses future assumptions, not historical data	Output only as good as the assumptions used

The Takeaway

Due to its relative simplicity and speed, traders often prefer it to the Black-Scholes and Monte Carlo models.

With SoFi, user-friendly options trading is finally here.

FAQ

Who developed the binomial model?

The binomial options pricing model was first suggested by William Sharpe in 1978, but the model’s development is associated with work done by John Cox, Stephen Ross, and Mark Rubinstein in 1979.

Are the Black-Scholes and binomial option pricing models the same?

No, these are two different models. The Black-Scholes model provides a numerical result based on inputs. The binomial options pricing model prices an asset based on a range of possible results. The binomial model is considered an iterative calculation since there is a range of possible outcomes to value options. The Black Scholes model uses fixed inputs to arrive at an option’s value.

How is the binomial option pricing model different from the Monte Carlo model?

The Monte Carlo model runs thousands of computer simulations to eventually arrive at an options price. The model first generates a random number based on a probability distribution. That number then uses additional option inputs like volatility and time to expiration to generate a stock price. The stock price at expiration is then used to calculate the value of the option. The result is only as good as the inputs used.

The model runs that process thousands of times, using different variables from the probability functions. To determine option pricing, the Monte Carlo model uses the average of all the calculated results.

Photo credit: iStock/David Petrus Ibars

SoFi Invest®

INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE

Aug

2023

Forex vs Options Compared and Examined

By Mike Zaccardi, CMT, CFA | Growing Wealth, invest, Investing | Comments Off

Foreign exchange trading, also known as forex or FX, is a global marketplace where participants trade national currencies.

Options trading allows participants to benefit from asset movements by trading puts and calls with less cash outlay than required to buy the underlying asset.

Both markets are characterized by the use of leverage with many other similarities as well as differences, and traders often engage in both markets.

What Is Options Trading?

Options are financial contracts that give the holder the right but not the obligation to buy or sell an underlying asset at a predetermined price and time, while creating a potential obligation for the option seller to buy or sell the underlying asset (if and when the buyer exercises the option contract).

Calls and puts are the two option types. Calls are the right to purchase an underlying asset while puts are the right to sell an underlying asset.

Options can be found on stocks, exchange-traded funds (ETFs), and on futures. With options trading vs. forex, an important distinction is that the options market is a derivatives market.

Recommended: Guide to Trading Options

Options trading online has increased in popularity now that commissions are so low. There has been huge growth in this market. Drawing traders to options is the potential for big profits over a short period. With options, you gain beneficial ownership of a large amount of an underlying security, like a stock, with a small amount of capital.

Some investors use options to protect their long-term holdings, such as a long stock position, by purchasing puts when they believe a near-term dip might take place. You can also increase your portfolio’s income by selling covered calls.

Overall, options trading can provide protection, generate income, and offer leverage. But options also come with risks.

When comparing options vs. forex, options trading can be more versatile than forex due to the vast number of options strategies. With forex trading, you simply go long or short a currency. Options trading offers the chance to profit in a variety of market conditions, too.

One downside to options trading is that it can take a long time to learn the ins and outs of options trading. Another drawback is that many options are illiquid, so it is hard to buy and sell quickly at a competitive price.

Finally, user-friendly options trading is here.^*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

*Check out the OCC Options Disclosure Document.

What Is Forex Trading?

Forex trading is the buying and selling of national currencies in a 24-hour market. In general, the forex market is considered the most liquid market in the world. While many currency pairs feature strong liquidity, there are still some that do not have a lot of buyers and sellers.

Trading forex vs. options often involves higher leverage and volatility risks.

When looking at forex vs. options, forex often offers more leverage. That means brokers allow you to trade with more capital than you have deposited in your account. With leverage comes the potential for massive gains, but also the risk of steep losses.

Brokers want to keep your risk in check, though. They often do that by requiring forex traders to enter stop-loss orders immediately once they take a position.

Another aspect that can make brokers nervous is volatility. The forex trading market can feature periods of relative calm followed by explosive volatility. When volatility strikes, currency pairs can become less liquid, leading to difficulties when attempting to exit trades. Forex options can be used to profit from volatility, however.

Comparing Forex vs Options

Let’s dive into some of the key similarities and differences in forex vs. options. It can help you decide which trading arena might suit your style better.

Similarities

A key similarity is that supply and demand drive both forex and options. If a tremendous amount of bullish sentiment arises, an option or currency pair can skyrocket in value. That can lead to big gains in both markets.

Before you jump into trading, doing your homework is important. In currency and derivatives markets, for every long there is a short, that means there is someone on the other side of the trade losing significantly. Remember always, that “someone” could be you.

Comparing options vs. forex, both offer leverage, but in different ways. Options, depending on the strategy, can allow you to control a large amount of stock with a small amount of capital. In forex trading, you can use margin to trade with leverage. You can even trade with up to 1,000x leverage with some forex brokers.

Today’s technology allows you to access many options and forex markets. That can make researching ideas and deciding on a single trade tough since there are so many tradable assets and strategies.

Both markets are regulated to help protect traders and brokers.

Differences

There are many differences in forex vs. options trading.

Forex involves trading currency pairs while options trading involves buying and selling contracts on an underlying asset. Hence, options are derivatives.

The options market is confined to normal trading hours while forex is a 24-hour market.

A final key difference in options vs. forex is liquidity. Many currency pairs have a large depth of buyers and sellers present, but there might just be a handful of traders in a particular options market.

There are also differences in forex vs. binary options, but you can trade forex binary options which are forex derivatives that pay out all or nothing.

Forex	Options
A 24-hour trading market of currency pairs	Contracts derived from an underlying asset
The most liquid trading market in the world	Trade during normal market hours
Ability to trade on leverage	Used for portfolio protection, income generation, and leverage when trading

Pros and Cons of Forex Trading

Pros of Forex Trading	Cons of Forex Trading
Stop losses help control risk	Losses can occur quickly due to leverage
Easier to trade and learn	Volatility can cause illiquidity on some pairs
Extremely liquid market pairs available	Lower middleman fees

Pros and Cons of Options Trading

Pros of Options Trading	Cons of Options Trading
Can be a highly leveraged play on stocks and other underlying assets	Many options are illiquid, which means high bid/ask spreads
Ability to profit from both price changes and time decay	You might not be approved to trade more complex options strategies
Traders can benefit from volatility spikes	Complex strategies can be difficult to learn

Is Forex or Options Trading Right for You?

Your trading preferences drive the decision of whether to engage in options or forex trading. Options offer defined risk strategies, but forex markets are often very liquid and trade 24 hours a day. You can also combine options trading with your stock trading account while forex could provide diversification.

Another market to consider is forex binary options. This market can feature the benefits of both forex and options, but you should always weigh the risks, too.

The Takeaway

There are many similarities and differences in options vs. forex. Options can be used on many underlying assets, and you can define your risk and reward strategy. When trading forex, you can profit from the rise and fall of national currencies and enjoy 24-hour markets. Both markets can be volatile, and there are risks associated with these strategies, so it’s important to recognize that before jumping in.

With SoFi, user-friendly options trading is finally here.

FAQ

Is options trading more profitable than forex?

When analyzing profit potential in forex trading vs. options trading, some contend that there is greater profit potential in the forex market due to very high liquidity and fast execution of trades. A key difference between forex vs. options is that forex can feature tremendous leverage, so huge profits can come quickly, but losses can also result in fast ruin.

Others say that options can be more profitable since this type of derivatives trading offers so many customized strategies that can have defined risk. You can also take advantage of time decay and volatility changes.

Is forex trading less risky than options trading?

It depends on your trading style. When analyzing forex vs. options trading, forex often requires position limits, so that can cap your risk. With options, risk is determined by your trading strategy and the positions you construct and execute. For example, selling a naked call features unlimited risk, but buying a deep in-the-money call can be relatively low risk.

A key difference in options vs. forex is that options markets have a finite time horizon — the option expiration date. Forex trading allows positions to be held longer. Another aspect of forex trading vs. options is that forex trading, despite being a liquid market, can have slippage costs when volatility strikes. That’s a risk to always keep in mind.

How do you invest in forex?

It is easy to start investing in forex. You simply open a brokerage account to hold a foreign currency. From there, you then fund your account, research a strategy, and execute an order. It’s important to always monitor your portfolio as the market can change quickly.

Photo credit: iStock/fizkes

SoFi Invest®

INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE

The Heston Model: Defined & Explained with Calculations

What Is the Heston Model?

How Does the Heston Model Work?

Heston Model Pros and Cons

Heston vs Black-Scholes Model

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

Other Option Pricing Models

Binomial Model

Risk-Neutral Probability

Monte Carlo Simulation

The Takeaway

FAQ

What is the Heston model used for?

Is the Heston model better than Black-Scholes?

What does stochastic local volatility mean?

Guide to Barrier Options

What Is a Barrier Option?

How Barrier Options Work

Pros and Cons of Barrier Options

Finally, user-friendly options trading is here.*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

Knock-In and Knock-Out Barrier Options

Knock-In

Knock-Out

Types of Barrier Options

Rebate Barrier Options

Turbo Warrant Barrier Options

Parisian Option

The Takeaway

FAQ

Are barrier options American or European?

How are barrier options valued?

Can you replicate barrier options?

Married Put Options Strategy: Defined & Explained

What Is a Married Put?

How Does a Married Put Work?

Maximum Profit

Breakeven

Maximum Loss

Finally, user-friendly options trading is here.*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

Married Put Example

Pros and Cons of Married Puts

Married Puts vs Covered Call

Strategies Similar to Married Puts

Protective Puts

Long Calls

Call Backspreads

The Takeaway

FAQ

Is a married put the same as a covered put?

Is a married put a good strategy?

What is the difference between puts and calls in options trading?

What the Binomial Option Pricing Model Is & How It Works

What Is the Binomial Option Pricing Model?

Assumptions of the Binomial Option Pricing Model

How Does the Binomial Model Work?

Binomial Option Pricing Model Calculations

Call Options

Put Options

Binomial Model Example

Assumptions

Generate the Binomial Tree

Calculate Final Option Values

Work Backward to Calculate Present Values

Finally, user-friendly options trading is here.*

Trade options with SoFi Invest on an easy-to-use, intuitively designed online platform.

Pros and Cons of the Binomial Model

Binomial Option Pricing Model vs Black-Scholes Model

Binomial Option Pricing Model vs Monte Carlo Model

The Takeaway

FAQ

Who developed the binomial model?

Are the Black-Scholes and binomial option pricing models the same?

How is the binomial option pricing model different from the Monte Carlo model?

Forex vs Options Compared and Examined

What Is Options Trading?

Finally, user-friendly options trading is here.*

Finally, user-friendly options trading is here.^*

Finally, user-friendly options trading is here.^*

Finally, user-friendly options trading is here.^*

Finally, user-friendly options trading is here.^*

Finally, user-friendly options trading is here.^*

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