Abstract
AbstractIt is the aim of Chap. 13 to introduce computational tools, which can be used to implement the functionals presented in this book. The first part of the chapter focuses on the non-central chi-squared distribution, which had arisen in the context of pricing financial derivatives in the Minimal Market Model introduced in Chap. 3. We provide both theoretical results and also a stable algorithm which can be used to compute the distribution function. In the second part of the chapter we focus on the non-central beta distribution, which had arisen in the context of pricing exchange options in the Minimal Market Model. Again, we provide both theoretical results but also a stable algorithm which can be used to compute the distribution function. The chapter concludes by discussing the inversion of Laplace transforms, which can be used to recover transition densities from the Laplace transforms presented throughout this book. We illustrate this approach in the context of the Minimal Market Model presented in Chap. 3.KeywordsShape ParameterLaguerre PolynomialIncomplete Gamma FunctionBessel ProcessIncomplete Beta FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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