It has been known for a long time that there is a close connection between stochastic processes and orthogonal polynomials. For example, N. Wiener 112] and K. Ito 56] knew that Hermite polynomials play an important role in the integration theory with respect to Brownian motion. In the 1950s D. G. Kendall 66], W. Ledermann and G. E. H. Reuter 67] 74], and S. Kar lin and J. L. McGregor 59] established another important connection. They expressed the transition probabilities of a birth and death process by means of a spectral representation, the so-called Karlin-McGregor representation, in...

Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of Levy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. Levy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of Levy-based models, and features many examples of how they may be used to solve problems in finance.
* Provides an introduction to the use of Levy...

Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Levy process. Working with Levy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Levy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same...

An introductory guide to using Levy processes for credit risk modeling

This introductory guide to Levy processes covers all types of credit derivatives, from the single-name vanilla derivatives to more complex structured credit risk products. It refines credit risk modeling with jump processes, a vital revision for today's tumultuous credit market. Readers will learn how the classical models can be improved with Levy processes. The book uses real market data to analyze and illustrate derivative structures and covers both the practical and theoretical underpinnings of Levy processes in...

The book draws on current research on model risk and parameter sensitivity of securitisation ratings. It provides practical ideas and tools that can facilitate a more informed usage of securitisation ratings. We show how global sensitivity analysis techniques can be used to better analyse and to enhance the understanding of the uncertainties inherent in ratings due to uncertainty in the input parameters. The text introduces a novel global rating approach that takes the uncertainty in the ratings into account when assigning ratings to securitisation products. The book also covers new...

Introducing a revolutionary new quantitative approach to hybrid securities valuation and risk management

To an equity trader they are shares. For the trader at the fixed income desk, they are bonds (after all, they pay coupons, so what's the problem?). They are hybrid securities. Neither equity nor debt, they possess characteristics of both, and carry unique risks that cannot be ignored, but are often woefully misunderstood. The first and only book of its kind, The Handbook of Hybrid Securities dispels the many myths and misconceptions about hybrid securities and arms you...