Problems and Solutions in Mathematical Finance v2 – Equity Derivatives

Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. * Review the fundamentals of equity derivatives * Work through problems from basic securities to advanced exotics pricing * Examine numerical methods and detailed derivations of closed-form solutions * Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.

Table of Contents:
Preface 5 1 Basic Equity Derivatives Theory 7 1.1 Introduction 7 1.2 Problems and Solutions 16 1.2.1 Forward and Futures Contracts 16 1.2.2 Options Theory 24 1.2.3 Hedging Strategies 38 2 European Options 81 2.1 Introduction 81 2.2 Problems and Solutions 93 2.2.1 Basic Properties 93 2.2.2 Black-Scholes Model 108 2.2.3 Tree Based Methods 205 2.2.4 The Greeks 233 3 American Options 279 3.1 Introduction 279 3.2 Problems and Solutions 283 3.2.1 Basic Properties 283 3.2.2 Time Independent Options 304 3.2.3 Time Dependent Options 317 4 Barrier Options 361 4.1 Introduction 362 4.2 Problems and Solutions 367 4.2.1 Probabilistic Approach 367 4.2.2 Reflection Principle Approach 400 4.2.3 Further Barrier Style Options 422 5 Asian Options 455 5.1 Introduction 455 5.2 Problems and Solutions 459 5.2.1 Discrete Sampling 459 5.2.2 Continuous Sampling 496 6 Exotic Options 545 6.1 Introduction 545 6.2 Problems and Solutions 546 6.2.1 Path Independent Options 546 6.2.2 Path Dependent Options 601 7 Volatility Models 661 7.1 Introduction 661 7.2 Problems and Solutions 666 7.2.1 Historical and Implied Volatility 666 7.2.2 Local Volatility 698 7.2.3 Stochastic Volatility 724 7.2.4 Volatility Derivatives 786 A Mathematics Formulae 805 B Probability Theory Formulae 815 C Differential Equations Formulae 831 Bibliography 839 Notation 845