دانلود کتاب روش‌های کمی در مالی همراه با شبیه‌سازی (۱): مقدمه‌ای بر تحلیل تصادفی و قیمت‌گذاری اختیار معامله

This book is the first volume of a two volume set that provides an introduction to stochastic analysis and quantitative finance, including theoretical and computational methods, for advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in the finance industry. The two volume set is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It is an expanded second edition of the previously published single volume edition titled Stochastic Analysis for Finance with Simulations. The first volume includes stochastic analysis, option pricing theory, optimal portfolio investment, bond pricing, with computer simulations for most theoretical ideas. The main topics of the second volume are numerical solution of the Black–Scholes–Merton partial differential equation and Monte Carlo methods for option pricing. Also included are ordinary and partial differential equations in general, stochastic differential equations, estimation of implied volatility, stochastic volatility models, and Fourier transform methods for option pricing. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the early chapters of the book and also in the appendices. Financial contracts are divided into two groups: The first group consists of primary assets such as shares of stock, bonds, commodities, and foreign currencies. The second group contains financial derivatives such as options and futures on the underlying assets belonging to the first group. A financial derivative is a contract that promises payment in cash or delivery of an asset contingent on the behavior of the underlying asset in the future. The goal of this book is to present mathematical methods for finding how much one should pay for a financial derivative. To understand the option pricing theory we need ideas from various disciplines ranging over pure and applied mathematics, not to mention finance itself. We try to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to theoretical exposition. The simulations in this book are not only used as a computational method in quantitative finance, but can also facilitate an intuitive and deeper understanding of theoretical concepts. Since the publications by Black, Scholes and Merton on option pricing in 1973, the theory of stochastic calculus, developed by Ito, has become the foundation for a new field called quantitative finance. In the first volume, stochastic calculus is presented starting from the theoretical first step. After introducing fundamental ideas in quantitative finance in Part I, we present mathematical prerequisites such as Lebesgue integration, probability, conditional expectation and stochastic processes in Part II. After that, basic properties of Brownian motion, Girsanov’s theorem and the reflection principle are given in Part III. In Part IV we introduce the Ito integral and Ito’s lemma, and then present the Feynman–Kac theorem. In Part V we present three methods for pricing options: the binomial tree method, the Black–Scholes–Merton partial differential equation, and the martingale method. In Part VI we analyze more examples of the martingale method, and study exotic options, American options and numeraires. In Part VII the variance minimization method for optimal portfolio investment is introduced for a discrete time model, and the Hamilton–Jacobi–Bellman equation is derived and used to solve optimization problems. In Part VIII some interest rate models are introduced and used in pricing bonds. In the appendices given in Part IX mathematical prerequisites are presented, including point set topology, linear algebra, ordinary differential equations, and partial differential equations, which are needed to understand the material in the main chapters. Basic Matlab and Python commands are explained in Appendix A and Appendix G, respectively. The graphs and diagrams in this book were plotted by the author using tikz, Matlab and Python, and the simulations were done using Matlab and Python.