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Put-Call Parity Calculator

Validate put-call parity relationships or solve for missing call or put options pricing parameters.

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Calculation Parameters

Specify your inputs below.

Calculated Result

Solved Put Value (from Parity) $2.62
Solved Call Value (from Parity) $9.73
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Expert Tip

Put-call parity defines the exact mathematical relationship between European calls, puts, stock prices, and discounted cash strikes.

How this Calculator Works

Uses the parity formula to calculate what the Call or Put value should be to prevent arbitrage.

Formula & Methodology

Call + K * e^(-r*t) = Put + Stock Call = Put + Stock - K * e^(-r*t) Put = Call + K * e^(-r*t) - Stock

Step-by-Step Calculation Example

Here is a step-by-step example showing how the calculations are performed:

If Stock = $100.00, Strike = $95.00, Time = 0.5 yrs, Rate = 4.5%, and Call = $9.73: - Solved Put = $9.73 + $95.00 * e^(-0.0225) - $100.00 = $2.62

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Detailed Insights & Expert Guide

โ„น๏ธ About this Calculation

This derivatives and options pricing calculator evaluates theoretical option premiums, implied volatility (IV), option Greeks (Delta, Gamma, Theta, Vega, Rho), multi-leg strategy risk profiles, and futures margin requirements using Black-Scholes and Cox-Ross-Rubinstein binomial models.

Variable Glossary

Input

Option Parameters

Underlying stock price (S), strike price (K), expiration days (T), volatility (ฯƒ %), and risk-free interest rate (r %).

Parameter

Greeks & Premium

Theoretical Call/Put price ($), Delta sensitivity (ฮ”), Theta daily decay (ฮ˜), and maximum profit/loss boundaries.

How to Calculate Step-by-Step

1

Step 1

Input current asset price, option contract strike price, and target expiration date.

2

Step 2

Specify implied or historical volatility percentage, dividend yield %, and risk-free treasury yield.

3

Step 3

Review calculated fair value option price, Greek risk sensitivities, break-even stock price, and payoff diagram matrix.

FAQ

What are the primary Option Greeks and what do they measure?
Delta (ฮ”) measures price sensitivity to underlying asset moves; Gamma (ฮ“) measures rate of Delta change; Theta (ฮ˜) measures daily time decay; Vega (ฮฝ) measures sensitivity to 1% volatility changes.
What is Put-Call Parity?
Put-Call Parity defines the static equilibrium relationship: Call Price - Put Price = Spot Price - Present Value of Strike Price. It prevents arbitrage between options and European spot markets.
Can option pricing models guarantee trading profits?
No. Black-Scholes and Binomial models assume continuous trading, constant volatility, and lognormal price distributions. Options trading involves substantial risk of capital loss due to leverage and volatility expansion.