Book Image

Introduction to R for Quantitative Finance

Book Image

Introduction to R for Quantitative Finance

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.

Related Content you might be interested in

Current Title:

Small book image
Introduction to R for Quantitative Finance
Nov, 2013 | 164 pages
No titles found
Table of Contents (17 chapters)
Introduction to R for Quantitative Finance
Introduction to R for Quantitative Finance
Credits
Credits
About the Authors
About the Authors
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Time Series Analysis
Time Series Analysis
Working with time series data
Linear time series modeling and forecasting
Cointegration
Modeling volatility
Summary
2
Portfolio Optimization
Portfolio Optimization
Mean-Variance model
Solution concepts
Working with real data
Tangency portfolio and Capital Market Line
Noise in the covariance matrix
When variance is not enough
Summary
3
Asset Pricing Models
Asset Pricing Models
Capital Asset Pricing Model
Arbitrage Pricing Theory
Beta estimation
Model testing
Summary
4
Fixed Income Securities
Fixed Income Securities
Measuring market risk of fixed income securities
Immunization of fixed income portfolios
Pricing a convertible bond
Summary
5
Estimating the Term Structure of Interest Rates
Estimating the Term Structure of Interest Rates
The term structure of interest rates and related functions
The estimation problem
Estimation of the term structure by linear regression
Cubic spline regression
Applied R functions
Summary
6
Derivatives Pricing
Derivatives Pricing
The Black-Scholes model
The Cox-Ross-Rubinstein model
Connection between the two models
Greeks
Implied volatility
Summary
7
Credit Risk Management
Credit Risk Management
Credit default models
Correlated defaults – the portfolio approach
Migration matrices
Getting started with credit scoring in R
Summary
8
Extreme Value Theory
Extreme Value Theory
Theoretical overview
Application – modeling insurance claims
Summary
9
Financial Networks
Financial Networks
Representation, simulation, and visualization of financial networks
Analysis of networks’ structure and detection of topology changes
Contribution to systemic risk – identification of SIFIs
Summary
References
References
Time series analysis
Portfolio optimization
Asset pricing
Fixed income securities
Estimating the term structure of interest rates
Derivatives Pricing
Credit risk management
Extreme value theory
Financial networks
Index
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...

Previous Section
End of Section 2
Next Section