A game theoretic approach to option valuation under Markovian regime-switching models

Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

In this paper, we consider a game theoretic approach to option valuation under Markovian regime-switching models, namely, a Markovian regime-switching geometric Brownian motion (GBM) and a Markovian regime-switching jump-diffusion model. In particular, we consider a stochastic differential game with two players, namely, the representative agent and the market. The representative agent has a power utility function and the market is a "fictitious" player of the game. We also explore and strengthen the connection between an equivalent martingale measure for option valuation selected by an equilibrium state of the stochastic differential game and that arising from a regime switching version of the Esscher transform. When the stock price process is governed by a Markovian regime-switching GBM, the pricing measures chosen by the two approaches coincide. When the stock price process is governed by a Markovian regime-switching jump-diffusion model, we identify the condition under which the pricing measures selected by the two approaches are identical.

Original languageEnglish
Pages (from-to)1146-1158
Number of pages13
JournalInsurance: Mathematics and Economics
Volume42
Issue number3
DOIs
Publication statusPublished - Jun 2008
Externally publishedYes

Keywords

  • C73
  • Esscher transform
  • G11
  • G13
  • Jump-diffusion model
  • Option valuation
  • Power utility
  • Regime switching
  • Stochastic differential game

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