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Option pricing with threshold diffusion processes. (English) Zbl 1414.91390

Summary: The threshold diffusion (TD) model assumes a piecewise linear drift term and piecewise smooth diffusion term, which can capture many nonlinear features and volatility clustering often observed in financial time series data. We solve the problem of option pricing with a TD asset pricing process by deriving the minimum entropy martingale measure, which is the risk-neutral measure closest to the underlying TD probability measure in terms of Kullback-Leibler divergence, given the historical regime-switching pattern. The proposed valuation model is illustrated with a numerical example.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
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