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Garman-Kohlhagen Calculator

Model foreign currency options values using the Garman-Kohlhagen adjustments for dual interest rates.

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Calculation Parameters

Specify your inputs below.

Calculated Result

Currency Call Value 0.0326
Currency Put Value 0.0102
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Expert Tip

The Garman-Kohlhagen model modifies Black-Scholes by discounting the spot exchange rate using the foreign interest yield.

How this Calculator Works

Calculates European currency call/put premiums under dual yield curves and volatility horizons.

Formula & Methodology

d1 = [ln(S/K) + (rd - rf + v^2 / 2)*t] / (v * sqrt(t)) d2 = d1 - v * sqrt(t) Call = S * e^(-rf*t) * N(d1) - K * e^(-rd*t) * N(d2)

Step-by-Step Calculation Example

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

If Spot = 1.12, Strike = 1.10, Days = 90, Dom = 4.0%, For = 3.0%, Vol = 12%: - Currency Call Value = 0.0326 - Currency Put Value = 0.0102

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Model option prices over step-by-step binomial lattices to evaluate American or European style contract options.

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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.