Choosing Rates and Volatility Inputs for Black-Scholes FX Options
Summary
The document discusses the inputs needed to price an FX option with a Black-Scholes style model when the trader has LIBOR quotes and historical exchange rates. One response suggests using the LIBOR rate nearest the option’s expiry, converting it to a continuously compounded rate, and estimating volatility from historical observations or a GARCH forecast. It also notes that the forecast horizon should match the option’s life.
A second response points out that FX options involve two currency interest rates, making the Garman–Kohlhagen model more appropriate than the single-rate equity formulation. The discussion cautions that LIBOR’s suitability as a risk-free proxy changed after the financial crisis, when LIBOR–OIS spreads became unstable; collateralized derivatives commonly use OIS-based curves, while treatment can differ for non-collateralized trades. These are practical guidelines rather than a full pricing workflow, and the choice of curves depends on market conventions and transaction details.
Key ideas
- A rate close to the option’s maturity can serve as an input, with compounding conventions handled consistently.
- Historical exchange-rate returns can be used to estimate volatility, while GARCH offers a forecast alternative.
- FX option valuation should account for the interest rates of both currencies, as in the Garman–Kohlhagen model.
- LIBOR is not universally an appropriate risk-free proxy; valuation conventions depend on collateralization and market conditions.
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Full text
# How to use the Black-Scholes formula with LIBOR rates? # How to use the Black-Scholes formula with LIBOR rates? I want to price an FX option using the Black-Scholes model, but I don't know the risk free rate, nor the volatility. I only know the LIBOR rates, the strike, and that the expiration day is 87 days from today. I also know the historical values of the exchange rate. I am not sure how to use the LIBOR rate and how to calculate the volatility. Do I use the 3 months LIBOR as a risk free rate? Do I have to convert the LIBOR to countinously compounded rate? ## Answer by Neeraj (score 4) https://quant.stackexchange.com/a/24417 You simply required 2 things: 1) Risk free rate, and 2) Standard Deviation. For the interest rate you can use LIBOR of nearest maturity. Convert your LIBOR rate into continuous compound rate by taking log. Additional: VIX also uses LIBOR as an proxy for risk free interest rate and they also select LIBOR of nearest maturity of option contract. Standard deviation can be easily computed from past historical data. You can also use GARCH model to forecast volatility for next 87 days and then take it average. ## Answer by Dhiraj Amarnani (score 0) https://quant.stackexchange.com/a/32970 Correct me if I am mistaken but since you are trying to price a forex option, wouldn't it be more appropriate to use the Garman and Kohlhagen extended Black-Scholes model since it better copes with the presence of the two interest rates associated with each currency respectively? "Also, LIBOR rates were considered a useful measure of the risk free rate (the rate taken closest to option expiration) due to its proximity to the overnight indexed swap (OIS) rates. Since 2007 however (and as a result of the financial crisis), the LIBOR-OIS spread has spiked and become unstable . John Hull has a very popular paper on this topic." http://www-2.rotman.utoronto.ca/~hull/DownloadablePublications/LIBORvsOIS.pdf John Hull said: "Most derivatives dealers now use interest rates based on overnight indexed swap (OIS) rates rather than LIBOR when valuing collateralized derivatives. For non-collateralized transactions, most dealers continue to use LIBOR rates for valuation." Most of this information was taken from a thread with the link below: Risk Free Rate vs LIBOR
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