Up and Out Put Option Calculator

An up-and-out put option is a type of exotic option that becomes invalid if the underlying asset's price reaches a specified barrier level. This calculator helps you evaluate the premium and potential profit of such an option.

What is an Up and Out Put Option?

An up-and-out put option is a financial instrument that combines the features of a put option with an automatic exercise barrier. The option holder has the right to sell the underlying asset at a predetermined strike price, but the option expires worthless if the asset's price reaches or exceeds a specified barrier level during the option's lifetime.

Key Features

Provides downside protection with an automatic exercise feature
Expires worthless if the asset price reaches the barrier
Typically more expensive than standard put options
Useful for investors who want to limit their risk exposure

Why Use an Up-and-Out Put Option?

This option type is particularly useful in several scenarios:

When you want to protect against a potential sharp rise in the asset price
When you believe the asset price will remain below a certain level
When you want to limit your risk while maintaining the potential for a large payoff

How to Calculate an Up and Out Put Option

The premium of an up-and-out put option can be calculated using advanced mathematical models, typically involving partial differential equations. However, for practical purposes, we can use a simplified approach that considers the following factors:

Simplified Premium Calculation

The premium (P) of an up-and-out put option can be approximated by:

P ≈ StandardPutPrice × (1 - k)

Where:

StandardPutPrice is the price of a standard European put option
k is a factor that depends on the barrier level and other parameters

Key Parameters

To calculate the premium, you need to consider several key parameters:

Current price of the underlying asset
Strike price of the option
Barrier level
Time to expiration
Risk-free interest rate
Volatility of the underlying asset

Potential Profit

The potential profit from an up-and-out put option can be calculated as:

Profit = Max(StrikePrice - ExercisePrice, 0) - Premium

Where ExercisePrice is the price at which the option is exercised, but only if the barrier level was not reached.

Example Calculation

Let's consider an example where:

Current stock price: $50
Strike price: $45
Barrier level: $55
Time to expiration: 30 days
Risk-free rate: 2%
Volatility: 30%

Using our simplified model and standard put option pricing formulas, we can estimate:

Standard put option price: $3.20
Barrier adjustment factor (k): 0.15
Up-and-out put premium: $2.72

If the stock price at expiration is $48 (below the barrier), the potential profit would be:

Profit = Max(45 - 48, 0) - 2.72 = 0 - 2.72 = -$2.72

However, if the stock price at expiration is $42 (below the barrier), the potential profit would be:

Profit = Max(45 - 42, 0) - 2.72 = 3 - 2.72 = $0.28

FAQ

What is the difference between an up-and-out put option and a standard put option?: An up-and-out put option has an automatic exercise feature and expires worthless if the underlying asset's price reaches a specified barrier level. Standard put options do not have these features.
Are up-and-out put options more expensive than standard put options?: Yes, up-and-out put options typically have higher premiums due to the added complexity and risk management features they provide.
When would it be appropriate to use an up-and-out put option?: This option type is suitable when you want to protect against a potential sharp rise in the asset price while maintaining the potential for a large payoff if the price remains below the barrier level.
How is the premium of an up-and-out put option calculated?: The premium is typically calculated using advanced mathematical models that consider factors such as the current price, strike price, barrier level, time to expiration, risk-free rate, and volatility of the underlying asset.
What happens if the asset price reaches the barrier level during the option's lifetime?: If the asset price reaches or exceeds the barrier level, the up-and-out put option expires worthless, and the premium paid is lost.

About this calculator

Written by Calculator Editorial TeamPractical calculator research and UX writing

Reviewed by Practical Tools ReviewFormula logic, assumptions, and usability checks

Updated June 26, 2026. Formulas, assumptions, and limitations are shown directly on this page.

Formula and Assumptions

The premium calculation uses a simplified model that approximates the price of an up-and-out put option. The formula accounts for the standard put option price and adjusts for the barrier feature.

Assumptions include:

Geometric Brownian motion for the underlying asset
Constant volatility and risk-free rate
No dividends on the underlying asset