Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.
This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.
An Introduction to the Mathematics of Financial Derivatives, Second Edition, introduces the mathematics underlying the pricing of derivatives. The increased interest in dynamic pricing models stems from their applicability to practical situations: with the freeing of exchange, interest rates, and capital controls, the market for derivative products has matured and pricing models have become more accurate. This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives. This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.
The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be considered as the finite-velocity counterpart of the classical Einstein-Smoluchowski's model of the Brownian motion in which the infinite speed of motion and the infinite intensity of the alternating directions are assumed. The book will be interesting to specialists in the area of diffusion processes with finite speed of propagation and in financial modelling. It will also be useful for students and postgraduates who are taking their first steps in these intriguing and attractive fields.
This textbook emphasizes the applications of statistics and probability to finance. It reviews the basics and advanced topics are introduced, including behavioral finance. The book serves as a text in courses, and those in the finance industry can use it for self-study.
Commodity Option Pricing: A Practitioner’s Guide covers commodity option pricing for quantitative analysts, traders or structurers in banks, hedge funds and commodity trading companies. Based on the author’s industry experience with commodity derivatives, this book provides a thorough and mathematical introduction to the various market conventions and models used in commodity option pricing. It introduces the various derivative products typically traded for commodities and describes how these models can be calibrated and used for pricing and risk management. The book has been developed with input from traders and examples using real world data, together with relevant up to date academic research. The book includes practical descriptions of market conventions and quote codes used in commodity markets alongside typical products seen in broker quotes and used in calibration. Also discussed are commodity models and their mathematical derivation and volatility surface modelling for traded commodity derivatives. Gold, silver and other precious metals are addressed, including gold forward and gold lease rates, as well as copper, aluminium and other base metals, crude oil and natural gas, refined energy and electricity. There are also sections on the products encountered in commodities such as crack spread and spark spread options and alternative commodities such as carbon emissions, weather derivatives, bandwidth and telecommunications trading, plastics and freight. Commodity Option Pricing is ideal for anyone working in commodities or aiming to make the transition into the area, as well as academics needing to familiarize themselves with the industry conventions of the commodity markets.
Tools for Computational Finance offers a clear explanation of computational issues arising in financial mathematics. The new third edition is thoroughly revised and significantly extended, including an extensive new section on analytic methods, focused mainly on interpolation approach and quadratic approximation. Other new material is devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation. New figures, more exercises, and expanded background material make this guide a real must-to-have for everyone working in the world of financial engineering.
Containing many results that are new or exist only in recent research articles, Interest Rate Modeling: Theory and Practice portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. The text begins with the mathematical foundations, including Ito’s calculus and the martingale representation theorem. It then introduces bonds and bond yields, followed by the Heath–Jarrow–Morton (HJM) model, which is the framework for no-arbitrage pricing models. The next chapter focuses on when the HJM model implies a Markovian short-rate model and discusses the construction and calibration of short-rate lattice models. In the chapter on the LIBOR market model, the author presents the simplest yet most robust formula for swaption pricing in the literature. He goes on to address model calibration, an important aspect of model applications in the markets; industrial issues; and the class of affine term structure models for interest rates. Taking a top-down approach, Interest Rate Modeling provides readers with a clear picture of this important subject by not overwhelming them with too many specific models. The text captures the interdisciplinary nature of the field and shows readers what it takes to be a competent quant in today’s market. This book can be adopted for instructional use. For this purpose, a solutions manual is available for qualifying instructors.
The Libor Market Model and its several extensions can be seen as state of the art in interest rate modeling. However, due to the ever increasing complexity of interest rate products, the high dimensionality of this approach starts to reach its limits from the computational side. This book is mainly concerned with a class of Markovian Yield Curve Models which try to overcome that disadvantage as they enable a low-dimensional deterministic and fast PDE valuation. The objective of this book is thereby threefold: - To illuminate in a compact way the connection between stochastic processes and partial differential equations as well as review the key features of arbitrage-free pricing. - To embed the here analyzed Markovian model class into the entire framework of interest rate models. - To present and implement robust numerical schemes, which enable an efficient computational treatment of risk-neutral product valuation by using PDE methods.