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

Chapter 3. Numerical Methods

In the previous chapter, we reviewed some of the key mathematical models used to describe the behavior of the underlying assets of financial derivatives. We saw, in particular, how these models are used to describe the future behavior of these assets based on the information we have today. These models are generally expressed in terms of SDEs and Partial Differential Equations (PDEs).

In this chapter, we are going to describe the three main numerical methods used in the financial markets today in the context of financial derivatives. They are a way to use actual numerical values to the abstract mathematical formulas we saw in the previous chapter. These numerical methods are as follows:

  • Monte Carlo (MC) simulation

  • Binomial Trees (BT)

  • Finite Difference Methods (FDM)

In the context of the Bento Box template, this chapter corresponds to box 3—numerical methods. There is a fourth family of methods, less frequently used, called quadrature methods, which are used for...