How to Calculate Put Option in Excel

Calculating put options in Excel is essential for options traders and financial analysts. This guide explains the put option formula, how to implement it in Excel, and provides a practical example.

What is a Put Option?

A put option is a financial contract that gives the buyer the right, but not the obligation, to sell an underlying asset at a predetermined price (the strike price) by a specified expiration date. Put options are used to hedge against potential price declines or to speculate on falling prices.

Key characteristics of put options include:

Right to sell, not obligation to sell
Specified strike price and expiration date
Used for hedging or speculative purposes
Price is influenced by volatility, time to expiration, and interest rates

Put Option Formula

The Black-Scholes model is commonly used to calculate the theoretical value of put options. The formula for the put option price is:

Put Option Price = S × N(-d1) - K × e^(-rT) × N(-d2)

Where:

S = Current stock price
K = Strike price
r = Risk-free interest rate
T = Time to expiration (in years)
σ = Volatility of the underlying asset
N(x) = Cumulative standard normal distribution function
d1 = (ln(S/K) + (r + σ²/2)T) / (σ√T)
d2 = d1 - σ√T

This formula calculates the theoretical value of a European-style put option. For American options, more complex models are needed.

Calculating Put Options in Excel

Step-by-Step Guide

Enter the current stock price in cell A1
Enter the strike price in cell B1
Enter the risk-free interest rate in cell C1 (as a decimal)
Enter the time to expiration in years in cell D1
Enter the volatility in cell E1 (as a decimal)
Calculate d1 using the formula in cell F1: =LN(A1/B1)+(C1+E1^2/2)*D1
Calculate d2 using the formula in cell G1: =F1-E1*SQRT(D1)
Calculate the put option price using the formula in cell H1: =A1*NORM.S.DIST(-F1,TRUE)-B1*EXP(-C1*D1)*NORM.S.DIST(-G1,TRUE)

Note: Excel's NORM.S.DIST function calculates the cumulative standard normal distribution. For older versions, you may need to use NORM.DIST with cumulative set to TRUE.

Using Excel's Built-in Functions

Excel provides the GBS function (Greek Black-Scholes) which can calculate option prices directly:

=GBS(S, K, r, σ, T, type)

Where type is "p" for put option and "c" for call option

For example: =GBS(A1, B1, C1, E1, D1, "p")

Worked Example

Let's calculate the put option price for a stock with the following parameters:

Parameter	Value
Current stock price (S)	$50
Strike price (K)	$55
Risk-free interest rate (r)	5% (0.05)
Time to expiration (T)	0.5 years
Volatility (σ)	20% (0.20)

Using the Black-Scholes formula:

Calculate d1: (ln(50/55) + (0.05 + 0.20²/2) × 0.5) / (0.20 × √0.5) ≈ -0.0953 / 0.1414 ≈ -0.674
Calculate d2: d1 - 0.20 × √0.5 ≈ -0.674 - 0.1414 ≈ -0.815
Calculate N(-d1): NORM.S.DIST(-(-0.674), TRUE) ≈ 0.747
Calculate N(-d2): NORM.S.DIST(-(-0.815), TRUE) ≈ 0.791
Put option price: 50 × 0.747 - 55 × e^(-0.05 × 0.5) × 0.791 ≈ 37.35 - 54.16 × 0.791 ≈ 37.35 - 42.88 ≈ $4.47

The calculated put option price is approximately $4.47.

Frequently Asked Questions

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

A put option gives the buyer the right to sell an asset, while a call option gives the right to buy. Puts are used to hedge against price declines, while calls are used to bet on price increases.

How accurate is the Black-Scholes model for put options?

The Black-Scholes model provides a good approximation for European-style options but may not be as accurate for American options or options with unusual expiration dates.

Can I use Excel to calculate put options for American-style options?

No, Excel's built-in functions are designed for European options. For American options, you would need to use more advanced financial modeling tools or programming.

What factors affect the price of a put option?

The price of a put option is influenced by the underlying asset's price, strike price, time to expiration, volatility, and interest rates.

How can I verify my put option calculations in Excel?

You can compare your results with financial calculators, trading platforms, or professional financial software to verify your calculations.