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Using Spot and Forward Rates in Garman–Kohlhagen Pricing

Article Quant Q&A · Author: hansvon
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Summary

The document answers which exchange rate to enter as the spot parameter when pricing an FX option with the Garman–Kohlhagen model. Its central point is to use the current spot rate; the forward rate for the option’s expiry is already implied by the model’s inputs and should not replace spot. The example concerns an MXN/USD option, but the answer is stated as a general input distinction.

The response is brief and provides no derivation, numerical price, or discussion of how interest rates determine the forward. It therefore offers a practical clarification rather than a complete explanation of the model. Readers still need to ensure that rate quotation conventions and the model’s other inputs are consistent with the currency pair.

Key ideas

  • Use the current spot exchange rate as the Garman–Kohlhagen spot input.
  • The forward rate is implied by the model’s inputs rather than substituted for spot.
  • The answer clarifies model inputs but does not derive the pricing relationship.

Tags

ForexOptionsDerivatives pricing
Full text
# Spot parameter of the Garman–Kohlhagen model


# Spot parameter of the Garman–Kohlhagen model












I need to price a FX option, let's say on MXN/USD with expiry in November in 8 months. The current forward rate for this expiry is ~20.89 MXN/USD while the current spot rate is 20.20. If I want to use the Garman-Kohlhagen model, should I use 20.89 or 20.20 as the spot parameter?

## Answer by João (score 1)

https://quant.stackexchange.com/a/82129

you should use the spot rate as the spot parameter, the fwd rate is already implied

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.