Stochastic processes with applications to finance - Kijima, Masaaki, 1957- (Boca Raton, FL : CRC Press, 2013)
'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 EditionA chapter on the change of measures and pricing of insurance productsMany examples of the change of measure technique, including its use in asset pricing theoryA section on the use of copulas, especially in the pricing of CDOs Two chapters that offer more coverage of interest rate derivatives and credit derivativesExploring 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'--
'Preface to the Second Edition When I started writing the first edition of this book in 2000, financial engineering was a kind of'bubble' and people seemed to rely on the theory often too much. For example, the credit derivatives market has grown rapidly since 1992, and financial engineers have developed highly complicated derivatives such as credit default swap (CDS) and collateralized debt obligation (CDO). These financial instruments are linked to the credit characteristics of reference assets' values, and they serve to protect risky portfolios as if they were an insurance against credit risks. People in finance industry found the instruments very useful and started selling/buying them without paying attention to the systematic risks involved in those products. An extraordinary result soon appeared as the so-called Lehman shock (the credit crisis). The financial crisis affected the economies in many countries even outside the U.S. Since then, mass-media started blaming people in finance industry, in particular financial engineers, because they have cheated financial markets just for their own benefits by making highly complicated products based on the mathematical theory. Of course, while the theory is used to create such awful derivative securities, those claims are not true at all. Who made mistakes were people who used the theory of financial engineering without thorough understanding of the risks and high ethical standards I believe that financial engineering is the useful tool for risk management, and indeed sensible people acknowledge the importance of the theory for hedging such risks in our economy. For example, G20 wants to enhance the content of Basel accords; but to do that, we need advanced theory of financial engineering'--
Includes bibliographical references and index.
Keywords: Financial engineering; Stochastic processes; Business mathematics