An Introduction to the Mathematics of Financial Derivatives

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

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.

"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." --