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

The Binomial Trees method


Binomial Trees (BT) can be traced to the work of (Cox, Ross, and Rubinstein 1979). Like MC methods, they are based on the idea of how the discretization of stock prices can jump up or down. Unlike the MC methods, BT are not based on simulation of many possible paths, but on the construction of a single path of possible future prices that bifurcates at every node. These prices, as well as their associated probabilities, constitute the tree. Once this tree is built, the prices of the underlying at maturity can be determined, and the the payoff at maturity can be then computed and discounted to the present time in order to determine the premium of the derivative.

Algorithm of the BT method

The BT method when applied to price derivatives is composed of three phases: the construction of the tree of prices (forward phase), the computation of the payoffs (maturity phase), and the discounting of the payoffs to the present time (backward phase). We will now explain the BT...