Put-Call Parity Calculator
C + PV(K) = P + S.
Arbitrage relationship: put = call + PV(strike) − stock.
How the Math Works
Put-call parity is a fundamental principle in options pricing that establishes a relationship between the prices of European call and put options with the same strike price and expiration date. The formula C + PV(K) = P + S expresses that the cost of a call option plus the present value of the strike price equals the cost of a put option plus the current stock price. Here, C represents the call option price, P is the put option price, S is the current stock price, and PV(K) is the present value of the strike price discounted at the risk-free rate. This equation reveals that these two portfolios should have equivalent values to prevent arbitrage opportunities in efficient markets.
Practical Applications
The put-call parity calculator is essential for identifying mispriced options in the market. Traders can input the current stock price, strike price, time to expiration, risk-free rate, and observed option prices to determine if an arbitrage opportunity exists. If the parity relationship doesn't hold, the calculator helps quantify the potential profit from simultaneously buying the undervalued portfolio and selling the overvalued one. Additionally, the calculator can be used to derive the implied interest rate from observed option prices, estimate dividend yields, or verify the theoretical consistency of option prices before executing trades.
Day-to-Day Use
Understanding put-call parity helps investors make more informed decisions about options trading and portfolio management. When you notice that a call option appears unusually cheap or expensive compared to its put counterpart, this principle helps you recognize whether it's a genuine market opportunity or a pricing anomaly. Even if you're not actively trading options, this knowledge provides insight into how different investment vehicles relate to each other and can help you better evaluate the relative value of various financial instruments in your retirement accounts or brokerage portfolios. The concept also serves as an educational tool for developing a deeper understanding of options pricing and market efficiency in everyday investing decisions.
FAQ
Violated?
Arbitrage opportunity exists.