Building and Deploying C++ Frameworks for the Monte Carlo Method - (code BDMC)

This course will be given by Dr. Joerg Kienitz and Dr. Daniel J. Duffy

This hands-on workshop applies C++ and related software design techniques to creating code that prices and hedges one-factor and multi-factor financial derivatives products using the Monte Carlo (MC) method. We discuss a representative number of one-factor and multi-factor option models and we show how they are approximated using MC and how to set up running C++ code to test these models.

Overview of Course

This practical course is for those professionals who design and implement MC models in C++. To this end, the course focuses on a number of essential issues:

• Modelling one-factor and multi-factor option models using MC
• Detailed review of underlying theory (RNG, SDE, distributions)
• State-of-the art customizable software frameworks for MC modelling
• Full C++ code for all models

What do you learn?

The main goal of this course is to show how to apply C++ to the pricing of derivatives using the Monte Carlo method. The emphasis is on customising a ready-made C++ framework to suit your own needs.

What do you receive?

In this course you get the course slides, CD with full source code and Daniel Duffy/Joerg Kienitz book "Monte Carlo Object-Oriented Frameworks in C++; Building Customisable and High-Performance Applications".
This means that you can practice at your own location and in your own time after the course. Your trainers are Dr. Joerg Kienitz and Dr. Daniel J. Duffy.

Please note: To participate in the course, you need to bring your own laptop computer with a C++ compiler (ideally, Microsoft's Visual Studio)

Course Contents

Part I: Fundamental Models and Building Blocks

Distributions

• Overview of distributions in finance
• Normal, gamma, Poisson and others
• Inverse cumulative distribution
• C++ implementation

Random Number Generation

• Uniform number generation
• Quasi-random number generation
• Non-uniform number generation
• C++ implementation

Review of Stochastic Processes

• Brownian motion
• Ornstein-Uhlenbeck
• Poisson and Compound Poisson processes
• Levy processes
• Variance Gamma
• Normal Inverse Gaussian
• Modelling stochastic processes in C++

An Introduction to Stochastic Differential Equations

• Motivating SDEs
• Linear and non-linear SDEs
• One-factor and n-factor SDEs
• Examples and categories of SDE
• Modelling SDE in C++

Part II: Numerical Methods

Quick Review of the Finite Difference Method

• Discretising ordinary and stochastic differential equations
• Stability and convergence
• Low-order and high-order methods

Numerical Approximation of SDE 

• Euler-Maruyama method
• Milstein method
• Predictor-Corrector method 
• Advantages and disadvantages

Advanced Numerical Methods

• Symplectic methods
• Splitting methods
• Designing C++ classes for SDE

Performance and Accuracy Issues

• Extrapolation
• Choosing a good scheme
• C++ and multi-processing

Part III: C++ Design Patterns and Software Frameworks

Overview and Background

• Design rationaleReview of the essential GOF (Gamma) patterns
• Essential system-level patterns
• Documentation: class diagrams and component diagrams

The Monte Carlo Framework: The Structure

• Blackboard architecture
• Mediator and Layers
• Customisation: using your own code in the frameworks
• Using object orientation and C++ templates

Walkthrough

• Approximation formulae
• Pricing barrier options in the framework
• Continuous and discrete monitoring
• Modelling option sensitivities
• Autocallable certificates

Part IV: Applications in Quantitative Finance

Overview

• Path-dependent options
• Taxonomy of path-dependent options
• Modelling option classes for path-dependency
• Performance and accuracy issues

Stochastic Volatility Models and Monte Carlo

• Introduction
• The Heston model
• Cliquet options
• C++ implementation

Early Exercise and American Options

• Longstaff-Schwarz regression method
• Dual method
• Case studies
• Performance improvements

Multifactor Models

• Introduction and overview
• Spread options and other correlated options

Presentation and Visualisation

• Excel output
• Integration with XLL
• Statistics and reporting

Prerequisites

We assume that you have C++ knowledge and that you have experience of the Monte Carlo method and its related topics. In this workshop the exercises take the form of integrating your code in the framework. The percentage theory/practice is approximately 80:20.

Who should attend?

Quantitative Analysts, Treasury stuff using MC, Asset Managers using MC, Risk Controller, IT Developers for Derivatives Pricing Models.

Duration, price, date, locations and registration