## Option pricing for pure jump processes with Markov switching compensators.(English)Zbl 1101.91034

The authors propose a model for asset prices that follow a jump process whose statistical behaviour is allowed switching between $$N$$ states. This is accomplished by employing Markov switching drift/compensator pairs. The resulting stock price process has the potential not only to capture any empirically observed behaviour (such as the term structures of moments) but it also allows diffusion-like behaviour allowing infinite activity around the origin. As it is not possible to obtain the density function in a closed form, a closed form expression for the characteristic function is derived instead, and an equivalent martingale representation is provided. The power of the characteristic function is demonstrated by utilizing it directly to value a large class of European options on a stock that follows this process, and to obtain optimal hedge ratios for these options.

### MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 60G44 Martingales with continuous parameter 60G51 Processes with independent increments; Lévy processes 60G10 Stationary stochastic processes 60J75 Jump processes (MSC2010)
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