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A tree approach to options pricing under regime-switching jump diffusion models. (English) Zbl 1335.91106

Summary: A simple, efficient tree approach is developed to price options in a very general regime-switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime-switching tree, we approximate Heston’s stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
60J75 Jump processes (MSC2010)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
91B70 Stochastic models in economics
91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
93E11 Filtering in stochastic control theory
93E20 Optimal stochastic control
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