Bounds and asymptotic approximations for utility prices when volatility is random

Ronnie Sircar, Thaleia Zariphopoulou

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

This paper is a contribution to the valuation of derivative securities in a stochastic volatility framework, which is a central problem in financial mathematics. The derivatives to be priced are of European type with the payoff depending on both the stock and the volatility. The valuation approach uses utility-based criteria under the assumption of exponential risk preferences. This methodology yields the indifference prices as solutions to second order quasilinear PDEs. Two sets of price bounds are derived that highlight the important ingredients of the utility approach, namely, nonlinear pricing rules with dynamic certainty equivalent characteristics, and pricing measures depending on correlation and the Sharpe ratio of the traded asset. The problem is further analyzed by asymptotic methods in the limit of the volatility being a fast mean-reverting process. The analysis relates the traditional market-selected volatility risk premium approach and the preference-based valuation techniques.

Original languageEnglish (US)
Pages (from-to)1328-1353
Number of pages26
JournalSIAM Journal on Control and Optimization
Volume43
Issue number4
DOIs
StatePublished - Aug 16 2005

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • Derivative pricing
  • Financial mathematics
  • Stochastic volatility
  • Utility indifference pricing

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