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Editor's Note: Options are not suitable for all investors. 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. Please see the Characteristics and Risks of Standardized Options.

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 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. Although 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 (with modifications). There are adjustments needed to use the binomial model based on which options are being priced. For this discussion, the focus will be on American options only.

Other assumptions in the model discussed herein include that the underlying asset pays no dividends, the interest rate is unchanging, there are no transaction costs, there are no taxes, and that the risk-free rate does not change.

It also assumes investors are risk-neutral.

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 before expiration. 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 (Cup) is the maximum of zero and the stock price (S) multiplied by the up factor (u) and reduced by the exercise price (Px).

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

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 less than the strike price.

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

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

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.

Assume that the stock may increase by 10% or decrease by 15% each week. 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.

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 below:

Because there are only two paths at each node, 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.

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.

Pros and Cons of the Binomial Model

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

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.

Due to its relative simplicity and speed, traders may prefer the binomial model to the Black-Scholes and Monte Carlo models.

SoFi’s options trading platform offers qualified investors the flexibility to pursue income generation, manage risk, and use advanced trading strategies. Investors may buy put and call options or sell covered calls and cash-secured puts to speculate on the price movements of stocks, all through a simple, intuitive interface.

With SoFi Invest® online options trading, there are no contract fees and no commissions. Plus, SoFi offers educational support — including in-app coaching resources, real-time pricing, and other tools to help you make informed decisions, based on your tolerance for risk.

Explore SoFi’s user-friendly options trading platform.

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

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Photo credit: iStock/David Petrus Ibars

Brokerage and self-directed investing products offered through SoFi Securities LLC, Member FINRA/SIPC. For a full listing of the fees associated with Sofi Invest, see our fee schedule.

Options involve substantial risk of loss and the possibility an investor may lose the entire amount invested. Before starting options trading, investors should be familiar with the Characteristics and Risks of Standardized Options . TTax implications with options should be considered. Consult your tax advisor to understand any impacts to your taxes.

Financial Tips & Strategies: The tips provided on this website are of a general nature and do not take into account your specific objectives, financial situation, and needs. You should always consider their appropriateness given your own circumstances.

Disclaimer: The projections or other information regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results.

Tax Information: This article provides general background information only and is not intended to serve as legal or tax advice or as a substitute for legal counsel. You should consult your own attorney and/or tax advisor if you have a question requiring legal or tax advice.

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For those who want to contribute to a Roth IRA but have an income that exceeds the limits, there’s another option. It’s called a backdoor Roth IRA, and it’s a way of converting funds from a traditional IRA to a Roth.

A Roth IRA is an individual retirement account that may provide investors with a tax-free income once they reach retirement. With a Roth IRA, investors save after-tax dollars, and their money generally grows tax-free. Roth IRAs also provide additional flexibility for withdrawals — once the account has been open for five years, contributions can typically be withdrawn without penalty.

But there’s a catch: Investors can only contribute to a Roth IRA if their income falls below a specific limit. If an individual’s income is too high for a Roth, they may want to consider a backdoor Roth IRA.

What Is a Backdoor Roth IRA?

Investors who aren’t eligible to contribute to a Roth IRA outright because they earn too much, can do so through a technique called a “backdoor Roth IRA.” This strategy involves contributing money to a traditional IRA and then converting it to a Roth IRA.

The government allows individuals to do this as long as when they convert the account, they pay income tax on any contributions they previously deducted and any profits made. Unlike a standard Roth IRA, there is no income limit for doing the Roth conversion, nor is there a ceiling to how much can be converted.

How Does a Backdoor IRA Work?

This is how a backdoor IRA typically works: An individual opens a traditional IRA and makes non-deductible contributions. They then convert the account into a Roth IRA. The strategy is generally most helpful to those who earn a higher salary and are otherwise ineligible to contribute to a Roth IRA.

Example Scenario

For instance, let’s say a 34-year-old individual wants to open a Roth IRA. Their tax-filing status is single and they earn $168,000 per year. Their income is too high for them to be eligible for a Roth directly (more on this below), but they can use the “backdoor IRA” strategy.

Recommended: Traditional Roth vs. Roth IRA: How to Choose the Right Plan

Income and Contribution Limits

In general, Roth IRAs have income limits. Whether you can make the full contribution depends on your modified adjusted gross income (MAGI) and tax-filing status.

Tax-filing status	Tax year	Modified adjusted gross income (MAGI)	Roth IRA contribution limit
Single	2025	• Less than $150,000 • $150,000 or more but less than $165,000 • $165,000 or more	• Full contribution • Partial contribution • Not eligible to contribute
Married, filing jointly	2025	• Less than $236,000 • $236,000 or more but less than $246,000 • $246,000 or more	• Full contribution • Partial contribution • Not eligible to contribute
Single	2026	• Less than $153,000 • $153,000 or more but less than $168,000 • $168,000 or more	• Full contribution • Partial contribution • Not eligible to contribute
Married, filing jointly	2026	• Less than $242,000 • $242,000 or more but less than $252,000 • $252,000 or more	• Full contribution • Partial contribution • Not eligible to contribute

There are also annual contribution limits for Roth IRAs, including catch-up contributions for those age 50 and older.

Tax year	Contribution limit for individuals under age 50	Contribution limit for individuals age 50 and up
2025	$7,000	$8,000
2026	$7,500	$8,600

How to Set Up and Execute a Backdoor Roth

Here’s the process to initiate and complete a backdoor Roth IRA.

•   Open a Traditional IRA.

•   Make a non-deductible contribution to the Traditional IRA.

•   Open a Roth IRA, complete any paperwork that may be required for the conversion, and transfer the money into the Roth IRA.

Tax Impact of a Backdoor Roth

If you made non-deductible contributions to a traditional IRA that you then converted to a Roth IRA, you won’t owe taxes on the money because you’ve already paid taxes on it. However, if you made deductible contributions, you will need to pay taxes on the funds.

In addition, if some time elapsed between contributing to the traditional IRA and converting the money to a Roth IRA, and the contribution earned a profit, you will owe taxes on those earnings.

You might also owe state taxes on a Roth IRA conversion. Be sure to check the tax rules in your area.

Another thing to be aware of: A conversion can move people into a higher tax bracket, so individuals may consider waiting to do a conversion when their income is lower than usual.

And finally, if an investor already has traditional IRAs, it may create a situation where the tax consequences outweigh the benefits. Here’s how: If an individual has money deducted in any IRA account, including SEP or SIMPLE IRAs, the government will assume a Roth conversion represents a portion or ratio of all the balances. For example, say the individual contributed $5,000 to an IRA that didn’t deduct and another $5,000 to an account that did deduct. If they converted $5,000 to a Roth IRA, the government would consider half of that conversion, or $2,500, taxable.

The tax rules involved with converting an IRA can be complicated. You may want to consult a tax professional.

Is a Backdoor Roth Right for Me?

Whether a backdoor Roth might be a good option depends on an individual’s unique situation. Below are some of the benefits and downsides to a backdoor Roth IRA to consider.

Benefits

High earners who don’t qualify to contribute under current Roth IRA rules may opt for a backdoor Roth IRA.

As with a typical Roth IRA, a backdoor Roth may also be an option when an investor expects their taxes to be lower now than in retirement. Investors who hope to avoid required minimum distributions (RMDs) when they reach age 73 might also consider doing a backdoor Roth.

Downsides

If an individual is eligible to contribute to a Roth IRA, it won’t make sense for them to do a backdoor conversion.

And because a conversion can also move people into a higher tax bracket, an investor may consider waiting to do a conversion in a year when their income is lower than usual.

For those individuals who already have traditional IRAs, the tax consequences of a backdoor Roth IRA might outweigh the benefits.

Finally, if you plan to use the converted funds within five years, a backdoor Roth may not be the best option. That’s because withdrawals before five years are subject to income tax and a 10% penalty.

Is a Backdoor Roth Still Allowed in 2025 or 2026?

Backdoor Roth conversions are still allowed for tax years 2025 and 2026.

There had been some discussion in previous years of possibly eliminating the backdoor Roth strategy, but this has not happened as yet.

The Takeaway

A backdoor Roth IRA may be worth considering if tax-free income during retirement is part of an investor’s financial plan, and the individual earns too much to contribute directly to a Roth.

In general, Roth IRAs may be a good option for younger investors who have low tax rates and people with a high income looking to reduce tax bills in retirement.

Prepare for your retirement with an individual retirement account (IRA). It’s easy to get started when you open a traditional or Roth IRA with SoFi. Whether you prefer a hands-on self-directed IRA through SoFi Securities or an automated robo IRA with SoFi Wealth, you can build a portfolio to help support your long-term goals while gaining access to tax-advantaged savings strategies.

Help build your nest egg with a SoFi IRA.

FAQ

What are the rules of a backdoor Roth IRA?

The rules of a backdoor Roth IRA include paying taxes on any deductible contributions you make; paying any other taxes you may owe for the conversion, such as state taxes; and waiting five years before withdrawing any earnings from the Roth IRA to avoid paying a penalty.

Is it worth it to do a backdoor Roth IRA?

It depends on your specific situation. A backdoor Roth IRA may be beneficial if you earn too much to contribute to a Roth IRA. It may also be advantageous for those who expect to be in a higher tax bracket in retirement.

What is the 5-year rule for a backdoor Roth IRA?

According to the 5-year rule, if you withdraw money from a Roth IRA before the account has been open for at least five years, you are typically subject to a 10% tax on those funds. The five-year period begins in the tax year in which you made the backdoor Roth conversion. There are some possible exceptions to this rule, however, including being 59 ½ or older or disabled.

Do you get taxed twice on backdoor Roth?

No. You pay taxes once on a backdoor IRA — when you convert a traditional IRA with deductible contributions and any earnings to a Roth. When you withdraw money from your Roth in retirement, the withdrawals are tax-free because you’ve already paid the taxes.

Can you avoid taxes on a Roth backdoor?

There is no way to avoid paying taxes on a Roth backdoor. However, you may be able to reduce the amount of tax you owe by doing the conversion in a year in which your income is lower.

Can you convert more than $6,000 in a backdoor Roth?

There is no limit to the amount you can convert in a backdoor Roth IRA. The annual contribution limits for IRAs do not apply to conversions. But you may want to split your conversions over several years to help reduce your tax liability.

What time of year should you do a backdoor Roth?

There is no time limit on when you can do a backdoor Roth IRA. However, if you do a backdoor Roth earlier in the year, it could give you more time to come up with any money you need to pay in taxes.

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SoFi Invest is a trade name used by SoFi Wealth LLC and SoFi Securities LLC offering investment products and services. Robo investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser. Brokerage and self-directed investing products offered through SoFi Securities LLC, Member FINRA/SIPC.

For disclosures on SoFi Invest platforms visit SoFi.com/legal. For a full listing of the fees associated with Sofi Invest please view our fee schedule.
Tax Information: This article provides general background information only and is not intended to serve as legal or tax advice or as a substitute for legal counsel. You should consult your own attorney and/or tax advisor if you have a question requiring legal or tax advice.
Options involve substantial risk of loss and the possibility an investor may lose the entire amount invested. Before starting options trading, investors should be familiar with the Characteristics and Risks of Standardized Options . TTax implications with options should be considered. Consult your tax advisor to understand any impacts to your taxes.

SOIN-Q226-113

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