Book Image

Introduction to R for Quantitative Finance

By : Gergely Daróczi, Michael Puhle, Edina Berlinger (EURO), Daniel Daniel Havran, Kata Váradi, Agnes Vidovics-Dancs, Agnes Vidovics Dancs, Michael Phule, Zsolt Tulassay, Peter Csoka, Marton Michaletzky, Edina Berlinger (EURO), Varadi Kata
Book Image

Introduction to R for Quantitative Finance

By: Gergely Daróczi, Michael Puhle, Edina Berlinger (EURO), Daniel Daniel Havran, Kata Váradi, Agnes Vidovics-Dancs, Agnes Vidovics Dancs, Michael Phule, Zsolt Tulassay, Peter Csoka, Marton Michaletzky, Edina Berlinger (EURO), Varadi Kata

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.
Table of Contents (17 chapters)
Introduction to R for Quantitative Finance
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Preface
Index

Mean-Variance model


The Mean-Variance model by Markowitz (Markowitz, H.M. (March 1952)) is practically the ice-cream/umbrella business in higher dimensions. For the mathematical formulation, we need some definitions.

They are explained as follows:

  • By asset , we mean a random variable with finite variance.
  • By portfolio, we mean the combination of assets: , where , and . The combination can be affine or convex. In the affine case, there is no extra restriction on the weights. In the convex case, all the weights are non-negative.
  • By optimization, we mean a process of choosing the best coefficients (weights) so that our portfolio meets our needs (that is, it has a minimal risk on the given expected return or has the highest expected return on a given level of risk, and so on).

Let be the random return variables with a finite variance, be their covariance matrix, and .

We will focus on the following optimization problems:

It is clear that is the variance of the portfolio and is the expected...