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The mathematics of derivatives securities with applications in MATLAB

Author: Mario Cerrato
Publisher: Hoboken : John Wiley & Sons Inc., 2012.
Series: Wiley finance series.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"The book is divided into two parts - the first part introduces probability theory, stochastic calculus and stochastic processes before moving on to the second part which instructs readers on how to apply the content learnt in part one to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility, and interest rate  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cerrato, Mario.
Mathematics of derivatives securities with applications in MATLAB.
Hoboken : John Wiley & Sons Inc., 2012
(DLC) 2012000873
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mario Cerrato
ISBN: 9781119973409 1119973406 9781119973416 1119973414 9781119973423 1119973422 9781118467398 1118467396
OCLC Number: 773371813
Notes: Machine generated contents note: Chapter 1 Introduction. Overview of MatLab. Using various MatLab's toolboxes. Mathematics with MatLab. Statistics with MatLab. Programming in MatLab. Part 1. Chapter 2 Probability Theory. 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. Chapter 3 Stochastic Processes. 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. Chapter 4 Ito Calculus and Ito Integral. Quadratic variation of 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. Part 2. Chapter 5 The Black and Scholes Economy and Black and Scholes Formula. 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. Chapter 6 Monte Carlo Methods for Options Pricing. Basic concepts and pricing European style options. Variance reduction techniques. Pricing path dependent options. Projections methods in finance. Estimations of Greeks by Monte Carlo methods. 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. Chapter 8 Exotic Options. Digital and binary. Asian options. Forward start options. Barrier options. Hedging barrier options. Chapter 9 Stochastic Volatility Models. 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. Chapter 10 Interest Rate Modeling. A general framework. Affine models. The Vasicek model. The Cox, Ingersoll & Ross Model. The Hull and White (HW) Model. Bond options.
Description: 1 online resource.
Contents: The Mathematics of Derivatives Securities with Applications in MATLAB; Contents; Preface; 1 An Introduction to Probability Theory; 1.1 The Notion of a Set and a Sample Space; 1.2 Sigma Algebras or Field; 1.3 Probability Measure and Probability Space; 1.4 Measurable Mapping; 1.5 Cumulative Distribution Functions; 1.6 Convergence in Distribution; 1.7 Random Variables; 1.8 Discrete Random Variables; 1.9 Example of Discrete Random Variables: The Binomial Distribution; 1.10 Hypergeometric Distribution; 1.11 Poisson Distribution; 1.12 Continuous Random Variables; 1.13 Uniform Distribution.
Series Title: Wiley finance series.
Responsibility: Mario Cerrato.

Abstract:

Fundamentals of Performance Technology is a practical how-to guide designed to help practitioners and students understand the science of performance technology and successfully implement  Read more...

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The book can be warmly recommended to readers who wish to learn the main methods of quantitative finance without delving into its mathematical foundations. (Zentralblatt MATH, 1 December 2012)

 
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