Interpolating and Extrapolating FX Volatility Smile Curves

Summary

The document asks how practitioners build a smooth foreign-exchange volatility smile from a small set of quoted points: at-the-money volatility, risk reversals, and strangles at two delta levels. It also asks which interpolation and extrapolation methods are commonly used to fill in volatility values between the quotes and beyond the observed range.

A specific extrapolation assumption is raised: preserve the smile curvature, represented by the strangle measure, while allowing the skew, represented by the risk reversal, to change outside the quoted region. The author asks how defensible this assumption is. No method, market example, comparative evidence, or answer is included, so the document identifies a modeling question rather than recommending a particular curve construction. The suitability of any extrapolation remains unevaluated in the source.

Key ideas

• FX volatility smiles are described through at-the-money, risk-reversal, and strangle quotes at selected delta levels.
• The document asks about methods for interpolating and extrapolating between and beyond a limited set of smile quotes.
• One proposed extrapolation keeps curvature constant while allowing skew to vary.
• The source provides no assessment or evidence for that assumption and recommends no specific technique.

Tags

# FX Smile Curve Extrapolation


# FX Smile Curve Extrapolation












- How a smooth smile curve is generated from 5 smile points : 10D RR, 25D RR, 10D SM, 25D SM and ATM? What are the commonly used extrapolation and interpolation techniques?

- I have seen people extrapolate smile curve beyond 5D points by assuming that the curvature (SM) stays the same and only skew(RR) changes. How fair is this assumption?

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