Put Call Parity Formula Calculator

Put Call Parity Formula:

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

Put Price (P):

USD

Stock Price (S):

USD

Strike Price (K):

USD

Interest Rate (r):

decimal

Time to Expiry (t):

years

Call Price (C):

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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:

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

Where:

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

Explanation: The formula shows that a call option is equivalent to buying a put option, buying the stock, and borrowing the present value of the strike price.

3. Importance of Put Call Parity

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

4. Using the Calculator

Tips: Enter all values in USD except for the interest rate (which should be in decimal form, e.g., 0.05 for 5%) and time (in years). All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: Does Put Call Parity apply to American options?
A: The exact formula applies only to European options. For American options, the relationship becomes an inequality due to early exercise possibilities.

Q2: What if Put Call Parity doesn't hold?
A: If the parity doesn't hold, arbitrage opportunities exist where traders can make risk-free profits by exploiting the price differences.

Q3: How does dividends affect Put Call Parity?
A: For stocks paying dividends, the formula must be adjusted to account for the present value of expected dividends during the option's life.

Q4: What's the practical use of Put Call Parity?
A: It's used for creating synthetic positions, pricing options, and identifying mispriced options in the market.

Q5: Can I use this for all option types?
A: This applies to standard European options. Exotic options or options with special features may not follow this parity.