Features Useful for practitioners and quants in the financial industry who need to make choices between pricing models of variance derivatives. Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products. Could be used as a textbook in a topic course on pricing variance derivatives at universities.

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.

This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass-Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context.

This book presents articles on original material from invited talks given at the 'IMS Workshop on Applied Probability' organized by the Institute of Mathematical Sciences at the Chinese University of Hong Kong in May 1999. The goal of the workshop was to promote research in applied probability for local mathematicians and engineers and to foster exchange with experts from other parts of the world. The main themes were mathematical finance and stochastic networks. The topics range from the theoretical study, e.g., ergodic theory and diffusion processes, to very practical problems, such as convertible bonds with market risk and insider trading. The wide scope of coverage in the book make it a helpful reference for graduate students and researchers, and for practitioners working in mathematical finance.