2014•Unpublished venueRequires access
Poisson Process
Eric Chin, Dian Nel, Sverrir Ólafsson
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Abstract
In mathematical finance, the important stochastic process is the Poisson process, used to model discontinuous random variables. This chapter discusses the Poisson process and some generalisations of it, such as the compound Poisson process and the Cox process that are widely used in credit risk theory as well as in modelling energy prices. In credit risk modelling, due to the stochastic process of the intensity, the Cox process can be used to model the random occurrence of a default event, or even the number of contingent claims in actuarial models. Another important generalisation of the Poisson process is to add a drift and a standard Wiener process term to generate a jump diffusion process. For the Poisson process, the outcome of the change of measure affects the intensity whilst for a compound Poisson process, the change of measure affects both the intensity and the distribution of the jump amplitudes.