Put Call Parity Calculator

Put-Call Parity Formula:

\[ C + K \times e^{-r \times t} = P + S \]

Call Price:

currency

Strike Price:

currency

Risk-Free Rate (r):

decimal

Time to Expiry (t):

years

Put Price:

currency

Stock Price:

currency

Parity Check:

Left Side (C + Ke^(-rt)):

Right Side (P + S):

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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 shows that the value of a call option implies a certain value for the corresponding put option and vice versa.

2. How Does the Calculator Work?

The calculator uses the Put-Call Parity formula:

\[ C + K \times e^{-r \times t} = P + S \]

Where:

\( C \) — Call option price
\( K \) — Strike price
\( r \) — Risk-free interest rate (as decimal)
\( t \) — Time to expiration (in years)
\( P \) — Put option price
\( S \) — Current stock price

Explanation: The formula shows that a portfolio consisting of a call option and cash equal to the present value of the strike price is equivalent to a portfolio consisting of a put option and the underlying stock.

3. Importance of Put-Call Parity

Details: Put-Call Parity is crucial for identifying arbitrage opportunities, understanding options pricing relationships, and constructing synthetic positions. It must hold in efficient markets to prevent risk-free profits.

4. Using the Calculator

Tips: Enter all required values in the same currency units. The calculator will verify whether the put-call parity relationship holds given your inputs. A small difference (less than 0.01) is considered acceptable due to rounding.

5. Frequently Asked Questions (FAQ)

Q1: Does put-call parity apply to American options?
A: No, put-call parity strictly applies only to European options (exercisable only at expiration). American options have a more complex relationship due to early exercise possibilities.

Q2: What if put-call parity doesn't hold?
A: Significant deviations may indicate arbitrage opportunities, pricing inefficiencies, or that the options are not European-style.

Q3: How does dividends affect put-call parity?
A: For stocks paying dividends, the present value of expected dividends must be subtracted from the stock price in the formula.

Q4: What's the practical use of put-call parity?
A: It's used to create synthetic positions, price options, and identify mispriced options in the market.

Q5: Why is the risk-free rate used?
A: The risk-free rate represents the time value of money for the cash component needed to replicate the option payoff.