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A PDE approach for risk measures for derivatives with regime switching |
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| Authors: | Robert J Elliott Tak Kuen Siu Leunglung Chan |
| Institution: | (1) Haskayne School of Business, Scurfield Hall, University of Calgary, 2500 University Drive NW, Calgary, T2N 1N4, AB, Canada;(2) Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK;(3) Department of Mathematics and Statistics, University of Calgary, Calgary, Canada |
| Abstract: | 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. |
| Keywords: | Risk measures Regime-switching PDE Regime-switching HJB equation Stochastic optimal control Esscher transform Delta-neutral hedging Jump risk American options Exotic options |
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