European option pricing with transaction costs and stochastic volatility: An asymptotic analysis

R. E. Caflisch, G. Gambino, M. Sammartino, C. Sgarra

Research output: Contribution to journalArticle

Abstract

In this paper, the valuation problem of a European call option in the presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion is shown to be the classical Black and Scholes solution, the correction terms appear at O(ε1/2) and O(ε). The optimal hedging strategy is then explicitly obtained for Scott's model.

Original languageEnglish (US)
Pages (from-to)981-1008
Number of pages28
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume80
Issue number4
DOIs
StatePublished - May 7 2014

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Keywords

  • asymptotic analysis
  • option pricing
  • stochastic volatility
  • transaction costs

ASJC Scopus subject areas

  • Applied Mathematics

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