#### 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 term structure of interest rates and related functions

A t-year zero-coupon bond with a face value of 1 USD is a security that pays 1 USD at maturity, that is, in t years time. Let denote its market value, which is also called the t-year discount factor. The function is called the discount function. Based on the no-arbitrage assumption, it is usually assumed that , is monotonically decreasing, and that . It is also usually assumed that is twice continuously differentiable.

Let denote the continuously compounded annual return of the t-year zero coupon bond; it shall be defined as:

The function is called the (zero coupon) yield curve.

Let denote the instantaneous forward rate curve or simply the forward rate curve, where:

Here is the interest rate agreed upon by two parties in a hypothetical forward loan agreement, in which one of the parties commits to lend an amount to the other party in t years time for a very short term and at an interest rate that is fixed when the contract is...