Stochastic Processes with Applications to Finance

This accessible text presents the mathematical theory of financial engineering using only basic mathematical tools that are easy to understand even for those with little mathematical expertise. This second edition covers several important developments in the financial industry. Along with many more examples, it includes a new chapter on the change of measures and pricing of insurance products, a new section on the use of copulas, and two new chapters that offer more coverage of interest rate derivatives and credit derivatives.

Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools that are easy to understand even for those with little mathematical expertise. This second edition covers several important developments in the financial industry.

New to the Second Edition

• A chapter on the change of measures and pricing of insurance products
• Many examples of the change of measure technique, including its use in asset pricing theory
• A section on the use of copulas, especially in the pricing of CDOs
• Two chapters that offer more coverage of interest rate derivatives and credit derivatives

Exploring the merge of actuarial science and financial engineering, this edition examines how the pricing of insurance products, such as equity-linked annuities, requires knowledge of asset pricing theory since the equity index can be traded in the market. The book looks at the development of many probability transforms for pricing insurance risks, including the Esscher transform. It also describes how the copula model is used to model the joint distribution of underlying assets.

By presenting significant results in discrete processes and showing how to transfer the results to their continuous counterparts, this text imparts an accessible, practical understanding of the subject. It helps readers not only grasp the theory of financial engineering, but also implement the theory in business.