Singular perturbations for boundary value problems arising from exotic options

Aytac Ilhan, Mattias Jonsson, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We study the pricing of three exotic derivative securities (barrier, lookback, and passport options) which can be characterized by boundary value PDE problems in the context of popular Markovian stochastic volatility models of stock prices. By extending the fast mean-reverting asymptotic analysis in [J.-P. Fouque, G. Papanicolaou, and K. R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, London, 2000], the usual "Greek" correction to the Black-Scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically. In the case of the passport option, the asymptotic method is effective in accounting for stochastic volatility effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem.

Original languageEnglish (US)
Pages (from-to)1268-1293
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number4
DOIs
StatePublished - Apr 2004

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Asymptotic approximations
  • Option pricing
  • Stochastic volatility

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