An Introduction to the Mathematics of Financial Derivatives

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

Autorentext

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.

Inhalt

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