This book will enable the reader to model, design and implement a range of financial models for derivatives pricing and asset allocation. The book will provide practitioners with the complete financial modeling workflow, from model choice, deriving analytic choice and/or approximate prices for simple options and calibration, to market data and exotic options pricing. Equity/Equity-Interest Rate Hybrid models, Interest Rate models and Asset Allocation are used as examples showing specific models with analysis of their features. The authors then go on to show how to price simple options and how to calibrate the models to real life market data and finally they discuss the pricing of exotic options. At the end of these sections the reader will be able to use the techniques discussed for equity derivatives and interest rate models in other areas of finance such as foreign exchange and inflation. The models discussed for derivatives pricing are: Heston / Bates Model Levy Models (Variance-Gamma, Normal Inverse Gaussian) Heston Hull White Model Libor Market Model SABR Model The models discussed for asset allocation are: Markowitz Model Black-Litterman Model Copula Models Parametric Models (Generalized Hyperbolic Models) Source code for all the examples is provided with implementation in C++ and/or C#. Contents Part 1 Theory Covers market data for the models and discusses the essential objects common to all models namely yield curves, volatility surfaces and time series. To successfully cope with these objects they show how to implement such structures in C++/C#. Chapter 1 Basic Financial Objects The first chapter introduces the financial objects used for modelling. Basic definitions from the markets are explained. Chapter 2 Probability Theory, Stochastic Analysis and Finance Basic theory and mathematical objects necessary for financial modelling using stochastic analytic and probabilistic concepts. Chapter 3 Transform Methods and Option Pricing This chapter deals with an important tool in finance - Transform Methods and its connection to option pricing. A well known one is the Fourier Transform but there are others like the Escher transformation used to study Levy processes. This will serve as a basis for many calibration applications in finance as well as for the applications considered in this book. Chapter 4 Simulation Simulation is one of the main tools in finance, e.g Monte Carlo Simulation is often the only method to price complex structured derivatives. Furthermore, some asset allocation models or value at risk calculation use simulation to model possible market scenarios. The authors give the basic facts necessary for successful application to financial models. Chapter 5 Optimization and Calibration This chapter reviews numerical methods for optimization and gives an introduction to local as well as global optimization algorithms. SQP, LFBGS, Levenberg-Marquardt and Differential Evolution are discussed and explained. Chapter 6 Numerical Integration and Quadrature Numerical Integration and Quadrature are applied to derive option prices using Fourier Transform or to compute convolution integrals numerically. Readers are given all the information necessary to implement the numerical methods. Part 2 Implementation (The Fundamentals) In Part 2 of the book the reader is shown how to implement the methods described in Part 1 of the book. Source code for the applications in Part 3 is also given. There is a focus on methods and design which is reusable and can be applied to many other financial problems. Chapter 7 Software Design Design patterns and concepts from object oriented programming which are used in this book are explained, by the end of the chapter the reader should be familiar with the design and the object oriented approach to be able to efficiently use the code. Chapter 8 Tools This chapter discusses necessary tools for implementing financial models e.g. the boost library and other frequently used libraries and toolkits like the Gnu Scientific Library or lpsolve. Chapter 9 Market Structures The implementation of the basic structures necessary for successfully handling complex models I shown e.g the implementation of classes for yield and volatility curves as well as basic structures for modelling option payoffs. Chapter 10 Monte Carlo Simulation A generic framework for implementation of the Monte Carlo method for option pricing and simulation - a short overview of a software system which as been previously developed by two of the authors (Duffy and Kienitz). Chapter 11 Optimization A generic framework for implementation of optimization methods. The implementation presented is flexible and easily extendable to use. Chapter 12 Numerical Integration In this chapter all the classes necessary for numerical integration are provided and the theoretical concepts of chapter 5 are coded and test cases for illustration and testing the accuracy are provided. Part 3 Applications Part 3 covers real life applications of the material presented in Part 1 and 2. Starting with a description of each model and proceeding on to pricing basic options which can be used to derive model parameters. After successfully calibrating the model the reader is shown how to price complex derivatives in this model. The models covered range from Equity to Interest Rates to Asset Allocation problems. Part 3a Equity and Hybrid Derivatives This part covers the most popular stochastic volatility models and hybrid models. It starts by introducing the Heston and the Bates stochastic volatility model to recover the skew and smile structures in equity markets, moves onto Equity-Interest Rate hybrid models e.g. the Heston-Hull White model. Finally, the authors show some pure jump models used for equity modelling, namely the NIG and VG model, adding stochastic volatility features, stochastic clocks, to this models they also considering multidimensional smile modelling. Chapter 13 Stochastic Volatility Models This chapter reviews the Heston and Bates stochastic volatility models as well as some pure jump processes for modelling. The authors consider a model where in contrast to the classical Black-Scholes-Merton model the rates and the volatility are stochastic and apply the Feynman-Kac theorem to derive analytic solutions which can be used to price European Call and Put options. In this chapter they also derive analytic approximation formulas for European Call and Put option and start applying the Feynman-Kac Theorem and applying Fourier transform methods to state the analytic formula. They then discuss and implement several numerical methods as direct integration or the Carr/Madan method using optimal alpha to numerically compute the prices using the derived analytical formula. Chapter 13 Deriving Model Parameters and Pricing Exotics To derive the model parameters from market data we apply a version of SQP and DE. After successfully calibrating the model we consider the pricing of Cliquet options including simple Cliquets, Swing Cliquets, Reverse Cliquets. We study Monte Carlo methods to perform the pricing of these derivatives and compare the prices of different models calibrated to the same market data. We further analyse hedging strategies