Call Put Parity Calculator

Call put parity is a fundamental principle 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 with the same strike price and expiration date. This calculator helps you verify whether the prices of call and put options satisfy the call put parity relationship.

What is Call Put Parity?

Call put parity is a theoretical relationship between the prices of European call and put options on the same underlying asset. It 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 based on the principle of arbitrage and assumes that there are no arbitrage opportunities in the market. In practice, call put parity can be used to:

Verify the fairness of option prices
Identify potential arbitrage opportunities
Understand the theoretical relationship between call and put options

Call put parity is most applicable to European options, which can only be exercised at expiration. For American options, which can be exercised at any time, the relationship is more complex due to the early exercise premium.

How to Use This Calculator

To use the call put parity calculator, follow these steps:

Enter the current price of the underlying asset (S)
Enter the strike price of the options (K)
Enter the price of the call option (C)
Enter the price of the put option (P)
Enter the risk-free interest rate (r)
Enter the time to expiration in years (T)
Click the "Calculate" button

The calculator will then display the call put parity value and explain whether the options prices satisfy the relationship.

Call Put Parity Formula

The call put parity relationship is expressed by the following formula:

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

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 = Base of the natural logarithm (approximately 2.71828)

The call put parity value is calculated as:

Call Put Parity Value = (C + K * e^(-rT)) - (P + S)

If the call put parity value is close to zero, the options prices satisfy the relationship. A positive value indicates that the call option is overpriced relative to the put option, while a negative value indicates that the put option is overpriced relative to the call option.

Example Calculation

Let's consider an example where:

Current stock price (S) = $50
Strike price (K) = $55
Call option price (C) = $5.00
Put option price (P) = $2.50
Risk-free interest rate (r) = 5% (0.05)
Time to expiration (T) = 0.5 years

Using the call put parity formula:

Call Put Parity Value = (5.00 + 55 * e^(-0.05 * 0.5)) - (2.50 + 50) = (5.00 + 55 * 0.9753) - 52.50 = (5.00 + 53.6915) - 52.50 = 58.6915 - 52.50 = 6.1915

The call put parity value is approximately $6.19, which indicates that the call option is overpriced relative to the put option by about $6.19.

Interpretation of Results

The call put parity value provides several insights:

If the value is close to zero, the options prices are in theoretical agreement with the call put parity relationship.
If the value is positive, the call option is overpriced relative to the put option, suggesting a potential arbitrage opportunity to buy the put option and sell the call option.
If the value is negative, the put option is overpriced relative to the call option, suggesting a potential arbitrage opportunity to buy the call option and sell the put option.

In practice, small deviations from zero are common due to market frictions, transaction costs, and other factors. Significant deviations may indicate inefficiencies in the market that could be exploited by arbitrageurs.

Frequently Asked Questions

What is the difference between call put parity and put call parity?

Call put parity and put call parity refer to the same theoretical relationship between call and put options prices. The terms are often used interchangeably, but "call put parity" is more commonly used in financial literature.

Can call put parity be used for American options?

Call put parity is most directly applicable to European options. For American options, the relationship becomes more complex due to the early exercise premium, which is not accounted for in the basic call put parity formula.

What does it mean if the call put parity value is not zero?

A non-zero call put parity value indicates a potential arbitrage opportunity. If the value is positive, the call option is overpriced, and if it's negative, the put option is overpriced. Traders can exploit these inefficiencies by buying the cheaper option and selling the more expensive one.

How often should I check call put parity?

Call put parity should be checked regularly, especially during periods of market volatility or when new options are issued. Traders and investors often monitor this relationship to identify arbitrage opportunities or to verify the fairness of option prices.