Call Put Parity Option Calculator

What is Call-Put Parity?

Call-Put Parity is a theoretical relationship between the prices of European call and put options with the same strike price and expiration date. It states that the difference in the price of a call option and a put option should equal the difference between the current stock price and the strike price, adjusted for the risk-free interest rate and time to expiration.

The principle is based on the idea that the right to buy (call) and the right to sell (put) should have equivalent value, adjusted for the cost of carrying the stock and the risk-free interest rate. This relationship is particularly useful for arbitrage strategies and for verifying the fairness of option prices.

How to Use the Calculator

Using the Call-Put Parity Option Calculator is straightforward. Follow these steps:

1. Enter the current stock price in the "Stock Price" field.
2. Enter the strike price of the options in the "Strike Price" field.
3. Enter the price of the call option in the "Call Option Price" field.
4. Enter the price of the put option in the "Put Option Price" field.
5. Enter the risk-free interest rate in the "Risk-Free Rate" field (as a decimal, e.g., 0.05 for 5%).
6. Enter the time to expiration in the "Time to Expiration" field (in years).
7. Click the "Calculate" button to see the results.

The calculator will display the calculated value of the left-hand side of the Call-Put Parity equation and compare it to the right-hand side. If the values are equal (within a small tolerance), the options are fairly priced according to the theory.

Call-Put Parity Formula

The Call-Put Parity formula is expressed as:

Where:

• Call Option Price - The price of the call option
• Put Option Price - The price of the put option
• Stock Price - The current price of the underlying stock
• Strike Price - The strike price of the options
• r - The risk-free interest rate
• t - The time to expiration (in years)

This formula shows the relationship between the prices of call and put options. If the options are European and the market is efficient, the left-hand side of the equation should equal the right-hand side.

Example Calculation

Let's walk through an example to illustrate how the Call-Put Parity Option Calculator works.

Suppose we have the following values:

• Stock Price: $50
• Strike Price: $55
• Call Option Price: $4.50
• Put Option Price: $6.00
• Risk-Free Rate: 5% (0.05)
• Time to Expiration: 0.5 years

Using the formula:

In this example, the left-hand side (-1.50) does not equal the right-hand side (-4.8765), which suggests that the options may not be fairly priced according to Call-Put Parity. This discrepancy could indicate an arbitrage opportunity or an inefficiency in the market.

Interpretation of Results

When you use the Call-Put Parity Option Calculator, you'll receive two key values:

1. Left-Hand Side (LHS): This is the difference between the call option price and the put option price.
2. Right-Hand Side (RHS): This is the difference between the stock price and the strike price, adjusted for the risk-free interest rate and time to expiration.

If the LHS equals the RHS (within a small tolerance), the options are fairly priced according to the theory. If they are not equal, there may be an arbitrage opportunity or a market inefficiency.

Limitations

While Call-Put Parity is a powerful tool, it has some limitations:

• It only applies to European options, not American options.
• It assumes no dividends are paid during the life of the option.
• It assumes a constant risk-free interest rate.
• Market imperfections can cause small discrepancies.

These limitations mean that Call-Put Parity should be used as a guide rather than an absolute rule. Traders should always consider other factors when making trading decisions.