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 FX Call (FX1)


In this example, we demonstrate the pricing of a plain vanilla European Call option on foreign exchange. Our aim here is to calculate the premium of this financial derivative.

The full details of the contract, including the choice of mathematical model and its numerical method, are shown in the following Bento Box template for European Call FX option (FX1).

Bento Box template for European Call FX option (FX1)

We proceed by completing the contents of the Bento Box in clockwise sense, starting from the top-left corner. The following are the steps to do so:

  1. Derivative contract: We first fill all the data of the contract, in particular the payoff function, which in our case is as follows:

    Equation 1

  2. Math model: We ought to select the mathematical model for the underlying, which in the case of currencies is the Garman-Kohlhagen model.

  3. Numerical method: We select the numerical method to be used and in this case, we choose the finite difference method.

  4. Algorithm...