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

Implied volatility


The Black-Scholes model is often criticized because of some shortcomings. One important problem is that the model assumes constant volatility for the underlying asset, which does not hold in reality. Furthermore, since it is not observable directly, the volatility is the most complicated parameter of the model to calibrate. Due to this difficulty, the Black-Scholes formula is often used in an indirect way for estimating the volatility parameter; we observe the market price of an option, then in view of all the other parameters we can search for σ that results a Black-Scholes price equal to the observed market price. This σ parameter is called the implied volatility of the option. As Riccardo Rebonato famously stated, implied volatility is "the wrong number to put in the wrong formula to get the right price" (Rebonato, 1999, p.78).

We will illustrate the calculation of implied volatility with the help of some Google options. The options are call options with the maturity...