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Interpolating FX Volatility Across Strike and Maturity

Article Quant Q&A · Author: Srini
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Summary

The document asks how to build a function that returns implied FX volatility for an arbitrary strike and maturity from quoted market points. The available inputs are 10-delta and 25-delta put and call volatilities, along with zero-delta straddle or at-the-money quotes, across several tenors. The author describes converting delta quotes into strikes using a flat yield curve for each currency, then seeks a way to interpolate between those observations.

No interpolation method or empirical evidence is supplied; the text is a question rather than a worked solution. It leaves open how to interpolate across strike and expiry, how to handle the FX volatility smile and term structure, and whether the assumed flat curves are adequate. These omissions mean it introduces the surface-construction problem but does not establish a recommended approach.

Key ideas

  • FX volatility is quoted at selected delta points and maturities.
  • Delta quotes can be converted into strike levels using rates for both currencies.
  • A pricing function needs a method to interpolate volatility across both strike and expiry.
  • The document poses the interpolation problem but does not provide or validate a solution.

Tags

ForexVolatilityDerivatives pricingStatistics
Full text
# How do we compute FX volatility for any given FX strike and time to maturity?


# How do we compute FX volatility for any given FX strike and time to maturity?












I want to implement a function which is passed two inputs: a strike and a time to maturity (which can be arbitrary within a specified range) and returns an FX volatility for this strike and maturity from a volatility surface estimated from FX data.

To give you context, I was given volatilies for 10delta put & call, 25delta put and call, ZDS/ATM for various tenors (O/N, 1W, 1Y etc). So using these and expiries I calculated my strike prices (using flat yield curve for both currencies) for each of the delta call and puts. Now I am asked to create a function to interpolate volatilities for any strike price and expiry

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