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On the Optimal Choice of Strike Conventions in Exchange Option Pricing

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  • Elisa Alòs

    (Departament d’Economia i Empresa, Universitat Pompeu Fabra and Barcelona GSE, c/Ramon Trias Fargas, 25-27, 08005 Barcelona, Spain)

  • Michael Coulon

    (Department of Business and Management, University of Sussex, Brighton BN1 9SL, UK)

Abstract

An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically optimal log-linear strike convention for exchange options under stochastic volatility models. This novel approach allows us to minimize the difference between the corresponding Margrabe computed price and the true option price. We show that this optimal convention does not depend on the specific stochastic volatility model chosen and, furthermore, that parameter estimation can be dramatically simplified by using market observables as inputs. Numerical examples are given that provide strong support for the new methodology.

Suggested Citation

  • Elisa Alòs & Michael Coulon, 2024. "On the Optimal Choice of Strike Conventions in Exchange Option Pricing," Mathematics, MDPI, vol. 12(19), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3028-:d:1487780
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    References listed on IDEAS

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    4. F. Antonelli & A. Ramponi & S. Scarlatti, 2010. "Exchange option pricing under stochastic volatility: a correlation expansion," Review of Derivatives Research, Springer, vol. 13(1), pages 45-73, April.
    5. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    6. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    7. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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