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 – European Call


In this first example, we consider the pricing of a plain vanilla European Call option. This example is exceedingly simple but crucial; it will serve as the building block for the rest of the option pricing problems to be solved with the Monte Carlo simulation.

The full characteristics of the contract, the choice of the mathematical model, and its numerical method are shown below in the Bento Box template:

Bento Box template for basic example: European Call

Our objective is to calculate the premium of this financial derivative. We proceed by completing the contents of the Bento Box in clockwise sense, starting from the top-left corner. We first fill all the data of the contract, in particular the payoff function, which for a simple European Call is as follows:

Secondly, we ought to select the mathematical model for the underlying, which in the case of equities is GBM. Third, we select the numerical method to be used as Monte Carlo simulation. Fourth, we construct...