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

Basic example – plain vanilla IRS (IR1)


In this example, we will demonstrate the pricing of a plain vanilla IRS. The full details of the contract, including the choice of the mathematical model and its numerical method, are shown in the following Bento Box template:

Bento Box template for basic example (IR1)

Our aim here is to calculate the net present value of this IRS, in particular a paying fixed-for-floating IRS. In this contract, the holder pays the fixed rate and receives the floating rate at regular intervals.

We proceed by completing the contents of the Bento Box in clockwise sense, starting from the top-left corner. First, we will fill all the data of the contract, in particular the payoff function, which in our case is as follows:

Equation 1

The present value of the IRS is the sum of the discounted future payments of the IRS. Being a paying IRS, we pay the fixed rate K and we receive the future floating rate L. This rate is fixed (that is, determined) at the beginning of the period...