Abstract

In Chapter 5 we apply the results of previous chapters for option pricing. The fundamental building block of all financial modelling is the concept of arbitrage-free and complete market. For the time- and space-continuous stochastic models the unique underlying process satisfying this concept is the geometric Brownian motion. In contrast, we suggest another approach to the continuous-time stochastic modelling of financial markets based on the telegraph processes. We construct a simple model, which is free of arbitrage and complete.

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