Currency Option Pricing Calculator (Garman-Kohlhagen)
Calculate the price of currency options using the Garman-Kohlhagen model. Designed for finance professionals seeking precise and authoritative calculations.
Option Inputs
How to Use This Calculator
Enter the spot rate, strike price, domestic and foreign interest rates, volatility, and time to maturity so the engine can price both the call and put side of a currency option using the Garman-Kohlhagen extension of Black-Scholes.
- Begin with real-time quotes for the underlying spot rate and select the strike price you care about.
- Supply the appropriate annualized interest rates for the domestic and foreign currencies—these are passed in as percentages.
- Use the volatility input to capture the market's implied swings for the currency pair, expressed in percent.
- Set the time to maturity in years; fractional values (e.g., 0.5 for six months) are accepted.
- Click Calculate or let the inputs refresh automatically to update the call and put quotes instantly.
Methodology & Data Source
The calculator implements the Garman-Kohlhagen model, which extends Black-Scholes for currency options by discounting each leg with the respective interest rate. It converts market inputs into the terms required for the analytic formulas and evaluates the cumulative normal distribution for the two key factors (d1 and d2).
The underlying model is widely accepted for vanilla currency derivatives; consult the original research (Garman & Kohlhagen, 1983) for additional detail and to reconcile these results with live quotes.
Glossary of Terms
- Spot Price (S0): Current quote for the base currency.
- Strike Price (X): Rate at which the option can be exercised.
- Domestic Interest Rate (rd): Annualized rate for the domestic currency.
- Foreign Interest Rate (rf): Annualized rate for the foreign currency.
- Volatility (σ): Expected annual volatility of the currency pair.
- Time to Maturity (T): Years remaining until expiration.
Step-by-Step Example
Assume a spot price of $1.20, a strike price of $1.25, a domestic rate of 2%, a foreign rate of 1%, a volatility of 15%, and a time to maturity of 1 year. Using the Garman-Kohlhagen model, the call and put option prices can be calculated as described in the formula section below.
Frequently Asked Questions (FAQ)
What is the Garman-Kohlhagen model?
It is a financial model used to price currency options by extending the Black-Scholes model.
How do I input the interest rates?
Interest rates should be entered as percentages (for example, enter 2 for 2%).
What does "volatility" mean?
Volatility represents how much the currency pair is expected to fluctuate over the remaining lifetime of the option.
Can I use this calculator for any currency pair?
Yes, you can price any currency option as long as you have the spot rate, strike price, rates, volatility, and maturity details.
How accurate are the results?
Results are as accurate as the inputs. Use reliable market data when populating the fields, and understand that real markets may include transaction costs and skew that this vanilla model does not capture.