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https://hdl.handle.net/2440/53573
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Type: | Journal article |
Title: | A PDE approach for risk measures for derivatives with regime switching |
Author: | Elliott, R. Siu, T. Chan, L. |
Citation: | Annals of Finance, 2008; 4(1):55-74 |
Publisher: | Springer-Verlag |
Issue Date: | 2008 |
ISSN: | 1614-2446 1614-2454 |
Statement of Responsibility: | Robert J. Elliott, Tak Kuen Siu and Leunglung Chan |
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 |
Description: | The original publication can be found at www.springerlink.com |
DOI: | 10.1007/s10436-006-0068-5 |
Published version: | http://dx.doi.org/10.1007/s10436-006-0068-5 |
Appears in Collections: | Aurora harvest 5 Mathematical Sciences publications |
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