The Mathematics of Derivatives Securities with Applications in MATLAB

Description

Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future.The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling.The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically.Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.Content: Chapter 1 An Introduction to Probability Theory (pages 1–23): Chapter 2 Stochastic Processes (pages 25–36): Chapter 3 Ito Calculus and Ito Integral (pages 37–53): Chapter 4 The Black and Scholes Economy (pages 55–66): Chapter 5 The Black and Scholes Model (pages 67–77): Chapter 6 Monte Carlo Methods (pages 79–89): Chapter 7 Monte Carlo Methods and American Options (pages 91–100): Chapter 8 American Option Pricing: The Dual Approach (pages 101–111): Chapter 9 Estimation of Greeks using Monte Carlo Methods (pages 113–120): Chapter 10 Exotic Options (pages 121–127): Chapter 11 Pricing and Hedging Exotic Options (pages 129–136): Chapter 12 Stochastic Volatility Models (pages 137–149): Chapter 13 Implied Volatility Models (pages 151–156): Chapter 14 Local Volatility Models (pages 157–166): Chapter 15 An Introduction to Interest Rate Modelling (pages 167–175): Chapter 16 Interest Rate Modelling (pages 177–184): Chapter 17 Binomial and Finite Difference Methods (pages 185–190):