Put-Call Parity Calculator

What is Put-Call Parity?

The put-call parity theorem is a fundamental concept in options pricing theory that establishes a relationship between the price of a call option and the price of a put option on the same underlying asset. This principle is based on the idea that the value of a call option and a put option should be equal when adjusted for the cost of carry and the risk-free rate.

Put-call parity is particularly useful for arbitrage opportunities. If the prices of call and put options do not satisfy the put-call parity equation, it creates an arbitrage opportunity where investors can profit by buying the cheaper option and selling the more expensive one.

How to Use This Calculator

Using the put-call parity calculator is straightforward. Follow these steps:

1. Enter the current price of the underlying asset (S).
2. Enter the strike price of the options (K).
3. Enter the price of the call option (C).
4. Enter the price of the put option (P).
5. Enter the risk-free interest rate (r) and the time to expiration (T) in years.
6. Click the "Calculate" button to verify put-call parity.

The calculator will display the calculated value of the put-call parity equation and indicate whether the options prices satisfy the put-call parity theorem.

Put-Call Parity Formula

The put-call parity theorem can be expressed by the following equation:

If the options prices satisfy this equation, they are said to be in put-call parity. If not, there is an arbitrage opportunity.

Example Calculation

Let's consider an example to illustrate how to use the put-call parity calculator. Suppose we have the following values:

• Current price of the underlying asset (S) = $50
• Strike price of the options (K) = $55
• Price of the call option (C) = $5
• Price of the put option (P) = $10
• Risk-free interest rate (r) = 5% (0.05)
• Time to expiration (T) = 1 year

Using the put-call parity formula:

In this example, the calculated value of the put-call parity equation is approximately $57.27, while the sum of the put option price and the underlying asset price is $60. The difference of $2.73 indicates that the options prices do not satisfy the put-call parity theorem, creating an arbitrage opportunity.

Interpretation of Results

The results from the put-call parity calculator can be interpreted as follows:

• If the calculated value of the put-call parity equation is equal to the sum of the put option price and the underlying asset price, the options prices satisfy the put-call parity theorem.
• If the calculated value is greater than the sum of the put option price and the underlying asset price, the call option is overpriced, and there is an arbitrage opportunity to buy the call option and sell the put option.
• If the calculated value is less than the sum of the put option price and the underlying asset price, the put option is overpriced, and there is an arbitrage opportunity to buy the put option and sell the call option.

Understanding the interpretation of the put-call parity results is crucial for identifying arbitrage opportunities and ensuring that options prices are fair and consistent with the underlying asset's value.