Abstract

This paper is concerned with the characterization of arbitrage-free dynamic stochastic models for the equity markets when Itô stochastic differential equations are used to model the dynamics of a set of basic instruments including, but not limited to, the underliers. We study these market models in the framework of the HJM philosophy originally articulated for Treasury bond markets. The main thrust of the paper is to characterize absence of arbitrage by a drift condition and a spot consistency condition for the coefficients of the local volatility dynamics.

Original languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalFinance and Stochastics
Volume13
Issue number1
DOIs
StatePublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Arbitrage-free term structure dynamics
  • Heath-Jarrow-Morton theory
  • Implied volatility surface
  • Local volatility surface
  • Market models

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