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Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities

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  • Matthias Muck

    (University of Bamberg)

Abstract

This paper addresses arbitrage-free FX smile construction from near-term implied volatility dynamics proposed by Carr (J Financ Econ, 120(1), 1–20, 2016). The approach is directly applicable to FX option market conventions. Prices of market benchmark contracts (risk reversals and butterflies) are identified as the roots of a cubic polynomial and ATM-volatility can be matched by construction. Implied volatilities are computed with respect to (non-premium adjusted) option deltas. The approach is compared to the Vanna Volga Approach, which does not guarantee arbitrage-free prices. An empirical application to a normal and a stress scenario demonstrates that arbitrage-free implied volatilities coincide with those from the Vanna Volga Approach when prices are interpolated between the $$\Delta$$ Δ 25-call and $$\Delta$$ Δ 25-put options. Differences are observed when implied volatilities are extrapolated to the wings. Empirically, these differences are particularly relevant in a stress scenario during the Coronavirus crises (2020).

Suggested Citation

  • Matthias Muck, 2022. "Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities," Review of Derivatives Research, Springer, vol. 25(3), pages 293-314, October.
    • Handle: RePEc:kap:revdev:v:25:y:2022:i:3:d:10.1007_s11147-022-09189-9
    DOI: 10.1007/s11147-022-09189-9
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    Cited by:

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    More about this item

    Keywords

    FX options; Smile construction; Delta; No-arbitrage; Derivatives;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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