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FX smile in the Heston model

In: Statistical Tools for Finance and Insurance

Author

Listed:
  • Agnieszka Janek

    (Wrocław University of Technology, Institute of Mathematics and Computer Science)

  • Tino Kluge

    (MathFinance AG)

  • Rafał Weron

    (Wrocław University of Technology, Institute of Organization and Management)

  • Uwe Wystup

    (MathFinance AG)

Abstract

The universal benchmark for option pricing is flawed. The Black-Scholes formula is based on the assumption of a geometric Brownian motion (GBM) dynamics with constant volatility. Yet, the model-implied volatilities for different strikes and maturities of options are not constant and tend to be smile shaped (or in some markets skewed). Over the last three decades researchers have tried to find extensions of the model in order to explain this empirical fact.

Suggested Citation

  • Agnieszka Janek & Tino Kluge & Rafał Weron & Uwe Wystup, 2011. "FX smile in the Heston model," Springer Books, in: Pavel Cizek & Wolfgang Karl Härdle & Rafał Weron (ed.), Statistical Tools for Finance and Insurance, chapter 4, pages 133-162, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18062-0_4
    DOI: 10.1007/978-3-642-18062-0_4
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