#### 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 Black-Scholes model

The assumptions of the Black-Scholes model (Black and Sholes, 1973, see also Merton, 1973) are as follows:

• The price of the underlying asset (S) follows geometric Brownian motion:

Here µ (drift) and σ (volatility) are constant parameters and W is a standard Wiener process.

• The market is arbitrage-free.

• The underlying is a stock paying no dividends.

• Buying and (short) selling the underlying asset is possible in any (even fractional) amount.

• There are no transaction costs.

• The short-term interest rate (r) is known and constant over time.

The main result of the model is that under these assumptions, the price of a European call option (c) has a closed form:

• ,
• ,

Here X is the strike price, T-t is the time to maturity of the option, and N denotes the cumulative distribution function of the standard normal distribution. The equation giving the price of the option is usually referred to as the Black-Scholes formula. It is easy to see from put-call parity that the price of a European...