#### Overview of this book

Introduction to R for Quantitative Finance will show you how to solve real-world quantitative fi nance problems using the statistical computing language R. The book covers diverse topics ranging from time series analysis to fi nancial networks. Each chapter briefl y presents the theory behind specific concepts and deals with solving a diverse range of problems using R with the help of practical examples.This book will be your guide on how to use and master R in order to solve quantitative finance problems. This book covers the essentials of quantitative finance, taking you through a number of clear and practical examples in R that will not only help you to understand the theory, but how to effectively deal with your own real-life problems.Starting with time series analysis, you will also learn how to optimize portfolios and how asset pricing models work. The book then covers fixed income securities and derivatives such as credit risk management.
Introduction to R for Quantitative Finance
Credits
www.PacktPub.com
Preface
Free Chapter
Time Series Analysis
Portfolio Optimization
Asset Pricing Models
Fixed Income Securities
Estimating the Term Structure of Interest Rates
Derivatives Pricing
Credit Risk Management
Extreme Value Theory
References
Index

## The Cox-Ross-Rubinstein model

The Cox-Ross-Rubinstein (CRR) model (Cox, Ross and Rubinstein, 1979) assumes that the price of the underlying asset follows a discrete binomial process. The price might go up or down in each period and hence changes according to a binomial tree illustrated in the following plot, where u and d are fixed multipliers measuring the price changes when it goes up and down. The important feature of the CRR model is that u=1/d and the tree is recombining; that is, the price after two periods will be the same if it first goes up and then goes down or vice versa, as shown in the following figure:

To build a binomial tree, first we have to decide how many steps we are modeling (n); that is, how many steps the time to maturity of the option will be divided into. Alternatively, we can determine the length of one time step t, (measured in years) on the tree:

If we know the volatility (σ) of the underlying, the parameters u and d are determined according to the following formulas...