Book Image

Advanced Quantitative Finance with C++

By : Alonso Peña, Ph.D.
Book Image

Advanced Quantitative Finance with C++

By: Alonso Peña, Ph.D.

Overview of this book

<p>This book will introduce you to the key mathematical models used to price financial derivatives, as well as the implementation of main numerical models used to solve them. In particular, equity, currency, interest rates, and credit derivatives are discussed. In the first part of the book, the main mathematical models used in the world of financial derivatives are discussed. Next, the numerical methods used to solve the mathematical models are presented. Finally, both the mathematical models and the numerical methods are used to solve some concrete problems in equity, forex, interest rate, and credit derivatives.</p> <p>The models used include the Black-Scholes and Garman-Kohlhagen models, the LIBOR market model, structural and intensity credit models. The numerical methods described are Monte Carlo simulation (for single and multiple assets), Binomial Trees, and Finite Difference Methods. You will find implementation of concrete problems including European Call, Equity Basket, Currency European Call, FX Barrier Option, Interest Rate Swap, Bankruptcy, and Credit Default Swap in C++.</p>
Table of Contents (17 chapters)
Advanced Quantitative Finance with C++
Credits
About the Author
Acknowledgments
About the Reviewer
www.PacktPub.com
Preface
Index

Advanced example – CDS (CR2)


In this second example, we consider the pricing of CDS. The details of the approach are shown in the following Bento Box template for the CDS:

Bento Box template for CDS (CR2)

A CDS is a financial contract between two counterparties A and B, in which one party pays to the other party to buy credit protection against the possible default of an underlying C.

In structure, the CDS is similar to the plain vanilla IRS, as it is composed of an exchange of cash flows between the parties. In a typical CDS with duration of five years, counterparty A pays B a series of premium payments at regular intervals upon an agreed notional. These payments will be made as long as underlying C "survives" (that is, doesn't go in default).

Counterparty B pays A a single contingent payment at the time of default of underlying C. The amount paid is equal to the notional minus the recovery rate. In mathematical terms, it can be expressed as follows:

Like in an IRS, the "price" of the contract...