Convergence of jump-diffusion models to the Black-Scholes model

Dowon Hong, In Suk Wee

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a jump-diffusion model for asset price which is described as a solution of a linear stochastic differential equation driven by a Lévy process. Such a market is incomplete and there are many equivalent martingale measures. We price a contingent claim with respect to the minimal martingale measure and construct a hedging strategy for the contingent claim in the locally risk-minimizing sense. We study the problem of convergence of option prices jointly with the costs from the locally risk-minimizing strategies when the jump-diffusion models converge to the Black-Scholes model.

Original languageEnglish
Pages (from-to)141-160
Number of pages20
JournalStochastic Analysis and Applications
Volume21
Issue number1
DOIs
Publication statusPublished - 2003

Keywords

  • Black-Scholes model
  • Jump-diffusion
  • Locally risk-minimizing hedging strategy
  • Lévy process
  • Minimal martingale measure

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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