Black Scholes Put Option Calculator Excel

The Black-Scholes Put Option Calculator Excel helps you determine the theoretical value of a put option using the Black-Scholes model. This calculator provides an Excel-compatible formula and guide to understand how put options are priced.

What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model used to determine the theoretical value of European-style options. It was developed by Fischer Black, Myron Scholes, and Robert Merton in 1973. The model assumes that the underlying asset follows a geometric Brownian motion with constant volatility and no dividends.

Put options give the holder the right, but not the obligation, to sell an underlying asset at a specified price (strike price) on or before a certain date (expiration date). The Black-Scholes model helps determine the fair value of these options based on several key factors.

Put Option Formula

The Black-Scholes formula for a put option is:

Put Option Price = S × N(-d1) - X × e^(-r × T) × N(-d2)

Where:

S = Current stock price
X = Strike price
r = Risk-free interest rate
T = Time to expiration (in years)
σ = Volatility of the stock
N(-d1) and N(-d2) are cumulative standard normal distribution functions

The d1 and d2 terms are calculated as follows:

d1 = (ln(S/X) + (r + σ²/2) × T) / (σ × √T)

d2 = d1 - σ × √T

These formulas are used to calculate the theoretical value of a put option based on the current market conditions and expected future price movements.

How to Use This Calculator

To use the Black-Scholes Put Option Calculator Excel:

Enter the current stock price (S) in dollars.
Enter the strike price (X) in dollars.
Enter the risk-free interest rate (r) as a decimal (e.g., 0.05 for 5%).
Enter the time to expiration (T) in years.
Enter the volatility (σ) as a decimal (e.g., 0.20 for 20%).
Click "Calculate" to compute the put option price.
Review the result and chart showing the option price over time.

The calculator will display the put option price and a chart showing how the option price changes over time.

Example Calculation

Let's calculate the put option price for the following inputs:

Current stock price (S) = $50
Strike price (X) = $55
Risk-free interest rate (r) = 0.05 (5%)
Time to expiration (T) = 0.5 years
Volatility (σ) = 0.30 (30%)

Using the Black-Scholes formula, the put option price is calculated to be approximately $4.25.

This means that the fair value of the put option with these parameters is $4.25.

Excel Formula

You can use the following Excel formula to calculate the Black-Scholes put option price:

=S*NORM.S.DIST(-d1,TRUE)-X*EXP(-r*T)*NORM.S.DIST(-d2,TRUE)

Where:

d1 = (LN(S/X)+(r+σ²/2)*T)/(σ*SQRT(T))
d2 = d1-σ*SQRT(T)

This formula uses Excel's built-in statistical functions to compute the cumulative standard normal distribution.

FAQ

What is the difference between a put option and a call option?

A put option gives the holder the right to sell an underlying asset at a specified price, while a call option gives the holder the right to buy the asset at a specified price. Put options are typically used for hedging or speculative purposes.

How does volatility affect the put option price?

Higher volatility generally increases the put option price because it implies a greater chance of the underlying asset's price falling below the strike price. Conversely, lower volatility tends to decrease the put option price.

Can the Black-Scholes model be used for American options?

The Black-Scholes model is specifically designed for European options, which can only be exercised at expiration. American options, which can be exercised at any time, require more complex models like the binomial options pricing model or Monte Carlo simulation.