Put Call Parity with Dividend Calculator

Put-Call Parity is a fundamental principle in options pricing that establishes a relationship between the price of European call and put options on a non-dividend-paying stock. When dividends are involved, this relationship becomes more complex but remains mathematically consistent.

What is Put-Call Parity?

Put-Call Parity is a theoretical relationship between the prices of European call and put options on the same underlying stock. It states that the difference between the price of a call option and a put option should equal the difference between the stock's price and the present value of the expected dividend.

For a non-dividend-paying stock, the basic Put-Call Parity formula is:

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 of the options
r = Risk-free interest rate
T = Time to expiration (in years)

This relationship is important because it provides a way to check for arbitrage opportunities in the options market.

Put-Call Parity with Dividend

When the underlying stock pays dividends, the Put-Call Parity formula becomes more complex. The dividend must be discounted to its present value and subtracted from the stock price.

The modified Put-Call Parity formula with dividend is:

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

Where:

D = Dividend amount
All other variables are as defined above

This formula accounts for the fact that the dividend will be received by the stockholder, reducing the value of the put option relative to the call option.

Note: This calculator assumes the dividend is paid before the option expires. If the dividend is paid after expiration, the Put-Call Parity relationship may not hold.

How to Use This Calculator

To use the Put-Call Parity with Dividend Calculator:

Enter the current stock price (S)
Enter the strike price of the options (K)
Enter the dividend amount (D)
Enter the risk-free interest rate (r) as a decimal (e.g., 0.05 for 5%)
Enter the time to expiration (T) in years
Click "Calculate" to see the results

The calculator will display the expected relationship between the call and put option prices according to Put-Call Parity with Dividend.

Example Calculation

Let's consider an example where:

Current stock price (S) = $50
Strike price (K) = $50
Dividend amount (D) = $2
Risk-free interest rate (r) = 5% or 0.05
Time to expiration (T) = 0.5 years (6 months)

Using the formula:

C - P = (50 - 2 * e^(-0.05*0.5)) - 50 * e^(-0.05*0.5)

Calculating the present value of the dividend:

D * e^(-rT) = 2 * e^(-0.025) ≈ 2 * 0.9753 ≈ 1.9506

Calculating the present value of the strike price:

K * e^(-rT) = 50 * e^(-0.025) ≈ 50 * 0.9753 ≈ 48.765

Putting it all together:

C - P ≈ (50 - 1.9506) - 48.765 ≈ 48.0494 - 48.765 ≈ -0.7156

This means the put option should be priced approximately $0.72 more expensive than the call option to satisfy Put-Call Parity with Dividend.

Frequently Asked Questions

What is the difference between Put-Call Parity and Put-Call Parity with Dividend?

Put-Call Parity is the basic relationship between call and put options on a non-dividend-paying stock. Put-Call Parity with Dividend accounts for the fact that the underlying stock pays dividends, which affects the relationship between the options.

Why is Put-Call Parity important?

Put-Call Parity is important because it provides a way to check for arbitrage opportunities in the options market. If the relationship is violated, it presents an opportunity to profit from the discrepancy.

What happens if the dividend is paid after the option expires?

If the dividend is paid after the option expires, the Put-Call Parity relationship may not hold because the dividend's effect on the option prices is no longer relevant.