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**Option pricing with regime switching by trinomial tree method.**
*(English)*
Zbl 1181.91315

Summary: We present a fast and simple tree model to price simple and exotic options in Markov regime switching model (MRSM) with multi-regime. We modify the trinomial tree model of P. P. Boyle [“Option valuation using a three-jump process”, Int. Options J. 3, 7–12 (1986)] by controlling the risk neutral probability measure in different regime states to ensure that the tree model can accommodate the data of all different regimes at the same time preserving its combining tree structure. In MRSM, the market might not be complete, therefore we provide some ideas and discussions on managing the regime switching risk in support of our results.

### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

91G60 | Numerical methods (including Monte Carlo methods) |

### Keywords:

trinomial method; regime switching; option pricing; exotic options; hedging risk of regime switching
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\textit{F. Lungyuen} and \textit{H. Yang}, J. Comput. Appl. Math. 233, No. 8, 1821--1833 (2010; Zbl 1181.91315)

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