An Introduction to the Mathematics of Financial Derivatives

by Ali Hirsa

Overview

An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. - Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning - Presented intuitively, breaking up complex mathematics concepts into easily understood notions - Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching

Product Details

ISBN-13:	9780123846839
Publisher:	Elsevier Science & Technology Books
Publication date:	12/18/2013
Sold by:	Barnes & Noble
Format:	eBook
Pages:	454
File size:	19 MB
Note:	This product may take a few minutes to download.

About the Author

Ali Hirsa is a professor and co-director of financial engineering at the Industrial Engineering & Operations Research at Columbia University. He is also Managing Partner at Sauma Capital, LLC and Senior Advisor at DV Trading, LLC where he was Managing Director and Global Head of Quantitative Strategy from June 2016 to August 2017. Ali was a Fellow at Courant Institute of New York University in the Mathematics of Finance Program from 2004 to 2014. He is co-inventor of "Methods for Post Trade Allocation (US Patent 8,799,146). The method focuses on allocation of filled orders (post-trade) on any security to multiple managed accounts which has to be fair and unbiased. Current existing methods lead to biases and the invention provides a solution to this problem.
Ali Hirsa is a professor and co-director of financial engineering at the Industrial Engineering & Operations Research at Columbia University. He is also Managing Partner at Sauma Capital, LLC and Senior Advisor at DV Trading, LLC where he was Managing Director and Global Head of Quantitative Strategy from June 2016 to August 2017. Ali was a Fellow at Courant Institute of New York University in the Mathematics of Finance Program from 2004 to 2014. He is co-inventor of “Methods for Post Trade Allocation” (US Patent 8,799,146). The method focuses on allocation of filled orders (post-trade) on any security to multiple managed accounts which has to be fair and unbiased. Current existing methods lead to biases and the invention provides a solution to this problem.

Table of Contents

1: Financial Derivatives: A Brief Introduction 2: A Primer on Arbitrage Theorem 3: Review of Deterministic Calculus 4: Pricing Derivatives: Models and Notations 5: Tools in Probability Theory 6: Martingales and Martingale Representations 7: Wiener Process, Levy Processes, and Rare Events 8: Differentiation in Stochastic Environments 9: Integration in Stochastic Environments 10: Ito's Lemma 11: The dynamics of Derivatives Prices: Stochastic Differential 12: Pricing Derivatives Products via Partial Differential Equations 13: Equivalent Martingale Measures 14: Equivalent Martingale Measures: Applications 15: Arbitrage Theorem in a New Setting 16: Term Structure Modeling and Related Concepts 17: Approaches to Modeling Term Structure 18: Conditional Expectations and PDEs 19: Derivative Pricing via Transform Techniques 20: Credit Spread and Credit Derivatives 21: Stopping Times and American-Style Derivatives 22: A Primer on Calibration and Estimation Techniques

What People are Saying About This

From the Publisher

This readable, informal overview of advanced financial engineering emphasizes intuition and supports it with common-sense mathematics.

Editorial Reviews

"This text introduces quantitative tools used in pricing financial derivatives to those with basic knowledge of calculus and probability. It reviews basic derivative instruments, the arbitrage theorem, and deterministic calculus, and describes models and notation in pricing derivatives, tools in probability theory, martingales and martingale representations, differentiation in stochastic environments, the Wiener and Lévy processes and rare events in financial markets…" —ProtoView.com, February 2014

"Ali Hirsa has done a superb job with this third edition of the very popular Neftci's An Introduction to the Mathematics of Financial Derivatives. New chapters and sections have been added covering in particular credit derivatives (Chapter 23) and jump processes and the associated partial integro-differential equations. The new material on numerical methods, in particular on Fourier techniques (Chapter 22) and calibration (Chapter 25), and added examples and exercises are very welcome. Overall, this new edition offers substantially more that the previous one in all of its chapters. This is a unique sophisticated introduction to financial mathematics accessible to a wide audience. Truly remarkable!" —Jean-Pierre Fouque, University of California, Santa Barbara

"The publication of this expansive and erudite text in a new edition by one of the most highly respected scholars in the field should be a welcome event for practitioners and academics alike." —Lars Tyge Nielsen, Columbia University

#"There are many books on mathematics, probability, and stochastic calculus, but relatively few focus entirely on the pricing and hedging of financial derivatives. I have used the second edition for finance and financial engineering classes for years, and will continue with the third edition; the book will no doubt remain a valuable reference for industry practitioners as well." —Robert L. Kimmel, National University of Singapore

"An excellent introduction to a wide range of topics in pricing financial derivatives with highly accessible mathematical treatment. Its heuristic style in explaining basic mathematical concepts relevant to financial markets greatly facilitates understanding the fundamentals of derivative pricing." —Seppo Pynnonen, Unversity of Vaasa

"What makes this introductory text unique for students or practitioners without a major in mathematics or physics is that it provides the most helpful heuristics while clearly stating how or why the concepts are useful for practical problems in finance. The timely additions on credit derivatives and PDEs provide considerable value-added in comparison to the second edition." —Mishael Milaković, University of Bamberg

From the Publisher