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Markovian regime-switching market completion using additional Markov jump assets. (English) Zbl 1280.91078

Summary: We discuss the use of some representation results for double martingales to value and hedge contingent claims in a Markovian regime-switching market. A set of \(N\) Markov jump assets is introduced to complete the Markovian regime-switching market. Using a representation for double martingales, we justify the completeness of the enlarged market. An equivalent martingale measure, or price kernel, in the enlarged market is then identified by a measure change. The option pricing formula and the hedging portfolio in the enlarged market is also discussed.

MSC:

91B25 Asset pricing models (MSC2010)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J27 Continuous-time Markov processes on discrete state spaces
91G20 Derivative securities (option pricing, hedging, etc.)
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