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Pricing FX Options with Negative Interest Rates

Article Quant Q&A · Author: user27607
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Summary

The exchange concerns pricing an EUR/GBP option when EURIBOR is negative and asks whether converting quoted rates to continuously compounded rates requires taking a logarithm. The answer clarifies that the relevant transformation is the logarithm of one plus the rate, rather than the logarithm of the rate itself. A negative rate can therefore still be transformed when the one-period gross rate remains positive.

The discussion is brief and offers no derivation, worked example, or option-pricing implementation. It does not compare Black–Scholes, Vanna–Volga, or Heston models, despite the question asking about them, and it does not specify compounding conventions, day counts, or market inputs. Treat it as a narrow clarification about rate conversion, not a complete guide to modeling or valuing FX options in a negative-rate setting.

Key ideas

  • Convert a simple quoted rate using the logarithm of one plus the rate, rather than the logarithm of the rate alone.
  • A negative rate can be compatible with this conversion if one plus the rate remains positive.
  • The reply does not provide a complete FX option pricing method or model implementation.

Tags

ForexOptionsDerivatives pricing
Full text
# Modeling FX option in a negative interest rate environment


# Modeling FX option in a negative interest rate environment












I am working on a project and I am trying to evaluate an FX option with EUR/GBP underlying. As the EURIBOR is negative, how can I do the pricing? I know I have to transform the interest rate, to switch to a continous interest rate (so I should apply log).

Please help me on this. Also, if you have codes for Black-Scholes, Vanna-Volga, Heston, I would really appreciate if you could share them with me.

Thank you!

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/33849

It shouldn't be a problem. You are taking log(1+rate) not log of rate itself.

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