Put-Call Parity Calculator

Put-Call Parity Formula:

\[ C = S + P - \frac{X}{(1 + \frac{R_f}{100})^{\frac{n_m}{12}}} \]

Spot Price of Underlying Asset:

Put Option Price:

Strike Price:

Risk-Free Rate of Return:

No. of Months:

months

Call Option Price:

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1. What is Put-Call Parity?

Put-Call Parity is a fundamental principle in options pricing that defines the relationship between the price of European call and put options with the same strike price and expiration date. It demonstrates that the price of a call option can be derived from the price of a put option and vice versa.

2. How Does the Calculator Work?

The calculator uses the Put-Call Parity formula:

\[ C = S + P - \frac{X}{(1 + \frac{R_f}{100})^{\frac{n_m}{12}}} \]

Where:

$ C $ — Call Option Price ($)
$ S $ — Spot Price of Underlying Asset ($)
$ P $ — Put Option Price ($)
$ X $ — Strike Price ($)
$ R_f $ — Risk-Free Rate of Return (%)
$ n_m $ — No. of Months

Explanation: The formula establishes that a portfolio consisting of a long call option and a short put option should be equivalent to a forward contract with the same strike price and expiration date.

3. Importance of Put-Call Parity

Details: Put-Call Parity is crucial for identifying arbitrage opportunities, pricing options accurately, and understanding the relationship between different financial instruments in options markets.

4. Using the Calculator

Tips: Enter all values in their respective units. Spot price, put option price, and strike price should be in dollars. Risk-free rate should be in percentage. Number of months should be a positive integer.

5. Frequently Asked Questions (FAQ)

Q1: Does Put-Call Parity apply to American options?
A: Put-Call Parity specifically applies to European options. For American options, the relationship becomes an inequality due to early exercise features.

Q2: What assumptions does Put-Call Parity make?
A: It assumes no arbitrage opportunities, no transaction costs, no dividends, and that options are European style (no early exercise).

Q3: How does dividends affect Put-Call Parity?
A: When the underlying asset pays dividends, the Put-Call Parity formula needs to be adjusted by subtracting the present value of expected dividends from the spot price.

Q4: What is the significance of the risk-free rate in the formula?
A: The risk-free rate accounts for the time value of money, discounting the strike price to its present value for comparison with current option prices.

Q5: Can Put-Call Parity be used for options pricing validation?
A: Yes, it's commonly used to check for mispriced options and identify potential arbitrage opportunities in the market.