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 Monte Carlo simulation method


Monte Carlo simulation is named after the famous casino in the principality of Monaco. It is the most widely used numerical method to price financial derivatives in the industry because of its simplicity, flexibility, and extensibility.

The basic idea of the method is to construct a simulation engine that will allow us to predict a number of possible ways (or trajectories) in which the underlying assets can evolve in the future. These trajectories can be thought of as potential economic or financial scenarios. With MC simulation, we attempt to answer questions such as "given the observed price of Vodafone stock today, what could be the likely prices of the stock each day for the next month?"

As we cannot be certain of the future evolution of prices, our result needs to be based on probability, and, thus, we need large number of samples. Using the stochastic models that we saw in the previous chapter to simulate one possible trajectory, with MC simulation,...