Put-Call Parity Calculator
This calculator helps traders and finance professionals determine the relationship between the price of European put and call options, ensuring they are priced correctly to avoid arbitrage opportunities. It is particularly useful for those involved in trading and options markets.
Calculator
Results
Data Source and Methodology
This calculator uses the standard put-call parity formula for European options as detailed in Wikipedia. All calculations are rigorously based on these formulas and data.
The Formula Explained
The put-call parity formula is expressed as:
Where \( C \) is the call option price, \( P \) is the put option price, \( S \) is the current stock price, \( X \) is the strike price, \( r \) is the risk-free interest rate, and \( T \) is the time to expiration.
Glossary of Terms
- Call Price: The current price of the call option.
- Put Price: The current price of the put option.
- Strike Price: The price at which the option can be exercised.
- Risk-Free Rate: The theoretical rate of return of an investment with zero risk.
- Time to Expiration: The time remaining until the option's expiration date.
How It Works: A Step-by-Step Example
Imagine a call option priced at $5, a put option priced at $3, a strike price of $50, a risk-free rate of 5%, and a time to expiration of 1 year. Plugging these values into the formula gives us a calculated parity, which helps verify the correctness of the option pricing.
Frequently Asked Questions (FAQ)
What is put-call parity?
Put-call parity is a financial principle that defines a relationship between the price of European call and put options with the same strike price and expiration.
Why is put-call parity important?
It helps ensure that options are correctly priced and that arbitrage opportunities are minimized.
Can put-call parity be applied to American options?
No, it is specifically applicable to European options due to their distinct exercise constraints.
How does the risk-free rate affect the calculation?
The risk-free rate impacts the present value of the strike price in the formula, influencing the parity.
What happens if put-call parity doesn't hold?
It may indicate mispricing in the options market, potentially leading to arbitrage opportunities.
Formula (LaTeX) + variables + units
','
\( C - P = S - Xe^{-rT} \)
- No variables provided in audit spec.
- Wikipedia — en.wikipedia.org · Accessed 2026-01-19
https://en.wikipedia.org/wiki/Put%E2%80%93call_parity
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.