Calculate Call Option Using Put Call Parity Calculator

What is Put-Call Parity?

Put-call parity is a fundamental principle in options trading that establishes a relationship between the price of a call option and the price of a put option with the same strike price and expiration date. The theorem states that the price of a call option plus the present value of the strike price should equal the price of a put option plus the present value of the underlying asset's current price.

This relationship is expressed mathematically and can be used to verify the fairness of option prices. If the put-call parity equation is not satisfied, it may indicate an arbitrage opportunity or a mispricing of the options.

How to Use the 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 risk-free interest rate (r).
4. Enter the time to expiration (T) in years.
5. Enter the price of the put option (P).
6. Click the "Calculate" button to determine the fair price of the call option.

The calculator will display the calculated call option price and provide an explanation of the result.

Put-Call Parity Formula

The put-call parity theorem is expressed by the following formula:

Where:

• C = Price of the call option
• P = Price of the put option
• S = Current price of the underlying asset
• K = Strike price of the options
• r = Risk-free interest rate
• T = Time to expiration in years
• e = Euler's number (approximately 2.71828)

This formula can be rearranged to solve for the call option price (C):

Example Calculation

Let's walk through 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
• Risk-free interest rate (r) = 5% or 0.05
• Time to expiration (T) = 0.5 years
• Price of the put option (P) = $4.50

Using the put-call parity formula:

The calculated price of the call option is approximately $0.81.

Limitations

While the put-call parity theorem is a powerful tool for options traders, it has some limitations:

• The theorem assumes no dividends are paid during the life of the option.
• It assumes no transaction costs or taxes.
• The theorem is based on the assumption of no arbitrage, which may not always hold in practice.
• Market imperfections and other factors can cause the put-call parity equation to be slightly off.

Despite these limitations, the put-call parity theorem remains a valuable tool for understanding the relationship between call and put options.