A PDE approach for risk measures for derivatives with regime-switching

Robert J. Elliott*, Tak Kuen Siu, Leunglung Chan

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Citations (Scopus)


This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black - Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options.

Original languageEnglish
Pages (from-to)55-74
Number of pages20
JournalAnnals of Finance
Issue number1
Publication statusPublished - Jan 2008
Externally publishedYes


  • American options
  • Delta-neutral hedging
  • Esscher transform
  • Exotic options
  • Jump risk
  • Regime-switching HJB equation
  • Regime-switching PDE
  • Risk measures
  • Stochastic optimal control

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