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Simulating the Evolution of the Implied Distribution

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  • George Skiadopoulos
  • Stewart Hodges

Abstract

Motivated by the implied stochastic volatility literature (Britten–Jones and Neuberger, forthcoming; Derman and Kani, 1997; Ledoit and Santa–Clara, 1998) this paper proposes a new and general method for constructing smile–consistent stochastic volatility models. The method is developed by recognising that option pricing and hedging can be accomplished via the simulation of the implied risk neutral distribution. We devise an algorithm for the simulation of the implied distribution, when the first two moments change over time. The algorithm can be implemented easily, and it is based on an economic interpretation of the concept of mixture of distributions. It can also be generalised to cases where more complicated forms for the mixture are assumed.

Suggested Citation

  • George Skiadopoulos & Stewart Hodges, 2001. "Simulating the Evolution of the Implied Distribution," European Financial Management, European Financial Management Association, vol. 7(4), pages 497-522, December.
    • Handle: RePEc:bla:eufman:v:7:y:2001:i:4:p:497-522
    DOI: 10.1111/1468-036X.00168
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    Cited by:

    1. Andreas Kaeck & Carol Alexander, 2013. "Stochastic Volatility Jump†Diffusions for European Equity Index Dynamics," European Financial Management, European Financial Management Association, vol. 19(3), pages 470-496, June.
    2. Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.

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