Put-Call Parity Calculator Excel

Put-Call Parity is a fundamental principle in options pricing that states the difference between the price of a call option and the price of a put option should equal the difference between the strike price and the current stock price, adjusted for the risk-free interest rate and time to expiration.

What is Put-Call Parity?

Put-Call Parity is a relationship between the prices of European call and put options with the same strike price and expiration date. It provides a theoretical relationship that should hold true in an efficient market with no arbitrage opportunities.

The principle states that the difference between the price of a call option and the price of a put option should equal the difference between the strike price and the current stock price, adjusted for the risk-free interest rate and time to expiration.

Put-Call Parity is particularly useful for verifying the consistency of option prices and identifying potential arbitrage opportunities when the relationship is violated.

Put-Call Parity Formula

The Put-Call Parity formula is expressed as:

C - P = S - K * e^(-rT)

Where:

C = Price of the call option
P = Price of the put option
S = Current stock price
K = Strike price
r = Risk-free interest rate
T = Time to expiration (in years)

This formula shows that the difference between the call and put option prices should equal the difference between the stock price and the strike price, adjusted for the time value of money.

How to Use the Calculator

Our Put-Call Parity Calculator allows you to verify the relationship between call and put option prices. Simply enter the required values and click "Calculate" to see if the relationship holds true.

The calculator will show you the calculated difference between the call and put option prices and compare it to the expected difference based on the stock price, strike price, interest rate, and time to expiration.

Example Calculation

Let's consider an example where:

Current stock price (S) = $50
Strike price (K) = $55
Risk-free interest rate (r) = 5% (0.05)
Time to expiration (T) = 0.5 years
Call option price (C) = $4.20
Put option price (P) = $2.80

Using the Put-Call Parity formula:

C - P = S - K * e^(-rT) 4.20 - 2.80 = 50 - 55 * e^(-0.05 * 0.5) 1.40 = 50 - 55 * 0.9753 1.40 = 50 - 53.6915 1.40 ≈ 1.3085

The calculated difference is approximately $1.31, which is close to the expected difference of $1.40. The slight discrepancy may be due to market inefficiencies or other factors.

Excel Formula

You can implement the Put-Call Parity calculation in Excel using the following formula:

=CALL_PRICE - PUT_PRICE = STOCK_PRICE - STRIKE_PRICE * EXP(-INTEREST_RATE * TIME_TO_EXPIRATION)

Replace the placeholders with your actual values to verify the Put-Call Parity relationship in Excel.

FAQ

What is the purpose of Put-Call Parity?

Put-Call Parity provides a theoretical relationship between call and put option prices that should hold true in an efficient market. It helps verify the consistency of option prices and identify potential arbitrage opportunities.

When is Put-Call Parity violated?

Put-Call Parity can be violated in markets with arbitrage opportunities, such as when the difference between call and put prices does not match the expected difference based on the stock price, strike price, interest rate, and time to expiration.

Can Put-Call Parity be used for all types of options?

Put-Call Parity is specifically applicable to European options, which can only be exercised at expiration. It is not directly applicable to American options, which can be exercised early.