Most books currently available on the subject require the reader to have some knowledge of the subject area and rarely consider computational applications such as MATLAB. This book stands apart from the rest as it covers complex analytical issues and complex financial instruments in a way that is accessible to those without a background in probability theory and finance, as well as providing detailed mathematical explanations with MATLAB code for a variety of topics and real world case examples.
Overview of MatLab
Using various MatLab `s toolboxes
Mathematics with MatLab
Statistics with MatLab
Programming in MatLab
Set and sample space
Sigma algebra, probability measure and probability space
Discrete and continuous random variables
Measurable mapping
Joint, conditional and marginal distributions
Expected values and moment of a distribution
Appendix 1: Bernoulli law of large numbers
Appendix 2: Conditional expectations
Appendix 3: Hilbert spaces.
Martingales processes
Stopping times
The optional stopping theorem
Local martingales and semi-martingales
Brownian motions
Brownian motions and reflection principle
Martingales separation theorem of Brownian motions
Appendix 1: Working with Brownian motions.
The construction of Ito integral with elementary process
The general Ito integral
Construction of the Ito integral with respect to semi-martingales integrators
Quadratic variation and general bounded martingales
Ito lemma and Ito formula
Appendix 1: Ito Integral and Riemann-Stieljes integral
The fundamental theorem of asset pricing
Martingales measures
The Girsanov Theorem
The Randon-Nikodym
The Black and Scholes Model
The Black and Scholes formula
The Black and Scholes in practice
The Feyman-Kac formula
Appendix 1: The Kolmogorov Backword equation
Appendix 2: Change of numeraire
Basic concepts and pricing European style options
Variance reduction techniques
Pricing path dependent options
Projections methods in finance
Chapter 7 American Option Pricing
A review of the literature on pricing American put options
Optimal stopping times and American put options
A dynamic programming approach to price American options
The Losgstaff and Schwartz (2001) approach
The Glasserman and Yu (2004) approach
Estimation of the upper bound
Cerrato (2008) approach to compute upper bounds.
Digital and binary
Asian options
Forward start options
Barrier options
Hedging barrier options
Square root diffusion models
The Heston Model
Processes with jumps
Monte Carlo methods to price derivatives under stochastic volatility
Euler methods and stochastic differential equations
Exact simulation of Greeks under stochastic volatility
Computing Greeks for exotics using simulations
A general framework
Affine models
The Vasicek model
The Cox, Ingersoll & Ross Model
The Hull and White (HW) Model
Bond options
