The Currency Option Pricing Calculator uses the Garman-Kohlhagen model to help finance professionals price currency options accurately. This tool is essential for traders and analysts dealing with international finance markets.
Currency Option Calculator
Results
Data Source and Methodology
All calculations are based strictly on the Garman-Kohlhagen model. For more details, refer to the original publication: Garman, M. B., & Kohlhagen, S. W. (1983). "Foreign currency option values". Journal of International Money and Finance, 2(3), 231-237.
The Formula Explained
\( C = S_0 e^{-r_f T} N(d_1) - X e^{-r_d T} N(d_2) \)
\( P = X e^{-r_d T} N(-d_2) - S_0 e^{-r_f T} N(-d_1) \)
Where \( d_1 = \frac{\ln(\frac{S_0}{X}) + (r_d - r_f + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}} \) and \( d_2 = d_1 - \sigma \sqrt{T} \)
Glossary of Terms
- Spot Price (S0): Current price of the underlying currency.
- Strike Price (X): Price at which the option can be exercised.
- Domestic Interest Rate (rd): Interest rate of the domestic currency.
- Foreign Interest Rate (rf): Interest rate of the foreign currency.
- Volatility (σ): Annualized volatility of the currency pair.
- Time to Maturity (T): Time remaining until the option's expiration, in years.
How It Works: A 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 follows...
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 input as percentages (e.g., 2 for 2%).
What does 'volatility' mean?
Volatility represents the degree of variation of a currency pair's trading price over time.
Can I use this calculator for any currency pair?
Yes, it is designed to handle any currency pair as long as you have the necessary market data.
How accurate are the results?
The results are as accurate as the inputs provided. Ensure that the data entered is from reliable market sources.
Formula (LaTeX) + variables + units
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\( C = S_0 e^{-r_f T} N(d_1) - X e^{-r_d T} N(d_2) \) \( P = X e^{-r_d T} N(-d_2) - S_0 e^{-r_f T} N(-d_1) \) Where \( d_1 = \frac{\ln(\frac{S_0}{X}) + (r_d - r_f + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}} \) and \( d_2 = d_1 - \sigma \sqrt{T} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
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.