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General approximation schemes for option prices in stochastic volatility models

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Author

  • Karl Larsson

Summary, in English

In this paper we develop a general method for deriving closed-form approximations of European option prices and equivalent implied volatilities in stochastic volatility models. Our method relies on perturbations of the model dynamics and we show how the expansion terms can be calculated using purely probabilistic methods. A flexible way of approximating the equivalent implied volatility from the basic price expansion is also introduced. As an application of our method we derive closed-form approximations for call prices and implied volatilities in the Heston [Rev. Financial Stud., 1993, 6, 327-343] model. The accuracy of these approximations is studied and compared with numerically obtained values.

Publishing year

2012

Language

English

Pages

873-891

Publication/Series

Quantitative Finance

Volume

12

Issue

6

Document type

Journal article

Publisher

Taylor & Francis

Topic

  • Economics

Keywords

  • Applied mathematical finance
  • Stochastic volatility
  • Option pricing
  • Stochastic applications

Status

Published

ISBN/ISSN/Other

  • ISSN: 1469-7696