An Introduction to the Mathematics of Financial Derivatives

Ali Hirsa, Salih N. Neftci

Academic Press, Dec 18, 2013 - Business & Economics - 454 pages

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

Contents

• 3 Review of Deterministic Calculus: 33
• Models and Notation: 55
• 5 Tools in Probability Theory: 65
• 6 Martingales and Martingale Representations: 87
• 7 Differentiation in Stochastic Environments: 111
• 8 The Wiener Process Lévy Processes and Rare Events in Financial Markets: 123
• 9 Integration in Stochastic Environments: 145
• 10 Itôs Lemma: 163
• 11 The Dynamics of Derivative Prices: 179
• Partial Differential Equations: 197
• 13 PDEs and PIDEsAn Application: 215
• Equivalent Martingale Measures: 231
• 15 Equivalent Martingale Measures: 253
• 16 New Results and Tools for InterestSensitive Securities: 269
• 17 Arbitrage Theorem in a New Setting: 277
• 18 Modeling Term Structure and Related Concepts: 301
• 19 Classical and HJM Approach to Fixed Income: 315
• 20 Classical PDE Analysis for Interest Rate Derivatives: 333
• 21 Relating Conditional Expectations to PDEs: 345
• 22 Pricing Derivatives via Fourier Transform Technique: 361
• 23 Credit Spread and Credit Derivatives: 373
• 24 Stopping Times and AmericanType Securities: 401
• 25 Overview of Calibration and Estimation Techniques: 415
• References: 437
• Index: 439
• Back Cover: 445

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.

Professor Neftci completed his Ph.D. at the University of Minnesota and was head of the FAME Certificate program in Switzerland. He taught at the Graduate School, City University of New York; ICMA Centre, University of Reading; and at the University of Lausanne. He was also a Visiting Professor in the Finance Department at Hong Kong University of Science and Technology. Known his books and articles, he was a regular columnist for CBN daily, the most influential financial newspaper in China. Salih Neftci was already suffering from gliosarcoma, a malignant brain cancer, while writing the second edition. It published just 5 months before his death on April 15, 2009.

Bibliographic information

• Title: An Introduction to the Mathematics of Financial Derivatives
• Authors: Ali Hirsa, Salih N. Neftci
• Edition: 3
• Publisher: Academic Press, 2013
• ISBN: 0123846838, 9780123846839
• Length: 454 pages
• Subjects: Business & Economics / Banks & Banking; Business & Economics / Finance / General; Business & Economics / Investments & Securities / General; Mathematics / Applied