Barcelona Financial Engineering Summer School 2008

PROGRAMME

Week 1

Week 2

Practitioner sessions

FX

Speakers
Philippe Lintern (RBS Global Financial Markets, Head of FX Complex Products Trading)
Dr. Adrian Campbell Smith (RBS Global Financial Markets, Senior trader, ex-quant)
Dr. Ben Nasatyr (RBS Global Financial Markets, Head of FX Quant Analysis)

Title
FX Trading and Modeling

Sessions

1. FX Options Market in General
1. Introduction to the FX options market (background, history, customers, taxonomy of products, liquidity, ...)
2. Pricing and risk managing FX barrier products
3. Quantitative challenges in FX options (taxonomy of models, implementation and performance issues etc)
2. Volatility and Correlation Products in FX
1. New and complex FX option products
2. Pricing and risk managing FX volatility and correlation products
3. Mathematics of volatility products

Equity

Speakers
Dr. Zareer Dadachanji (Credit Suisse, Senior Quant)

Title
A tour through the world of equity derivatives modeling

Sessions

1. Stocks, indices and futures - we call it "Delta One"
2. Variations on a theme of vanilla options
3. Exotic options with exotic names
4. The latest fashions in equity derivatives

Abstract
This course is an introduction to the world of equity derivatives. We describe and discuss a wide variety of popular products, explaining in each case the benefits offered by the product to the investor. We examine the various challenges with which the products present us, and the modeling methods we have developed to deal with them.

IRD

Speakers
Javier Vindel (CitiBank, IRD Quant)

Title
The practice of IR Derivatives modeling: implementing the Markov functional model

Sessions

1. Taxonomy of products
2. Trading conventions, liquidity and modeling of basic products
3. Problems in the pricing of exotic products
4. The Markov functional model

Abstract
This set of lectures will present the practical aspects related to the modeling and implementation of interest rate derivatives in an investment banking operation. After describing the products and problems at hand we will present some of the basic pricing techniques for the more vanilla products together with details on their quoting and trading characteristics. More exotic models require more complex models, we will describe some of these and their raison d'etre on the second half of the course, special attention will be devited to the Markov Functional model and its implementation.

Academic Sessions

Speakers
Prof. Daniel Duffy (DataSim, Netherlands)
Author of the best-seller Finite Difference Methods in Financial Engineering, John Wiley and Sons 2006

Title
Advanced PDE Techniques for Option Pricing and Finite Difference Method

Sessions

1. Introduction: What is a PDE?, PDEs in Finance, Solution of PDE, Theory of FDM (stability, convergence), Solving FD schemes
2. One-factor Models: The Black Scholes PDE, Plain, barrier and other one-factor models, Early exercise and free boundaries , Disc
ontinuous boundary and terminal conditions, Small volatility and exponentially fitted methods
3. Two and three-factor Models: Where do we need 2-factor PDE?, Introduction to the Splitting method, Solving two-factor problems
4. Applications and special Issues: Pricing with local and stochastic volatility, The Heston model, Calibration issues

Abstract
The 4 hour set of lectures is an introduction to PDE/FDM methods to price one-factor and multi-factor equity plain and American options. We give a complete overview (at a high level) of the status of this modeling technique based on the author’s experience in this area (documented in Finite Difference Methods in Financial Engineering).

Speakers
Prof. Daniel Dufresne (Melbourne, Australia)

Title
The distribution of realized volatility in stochastic volatility models

Sessions

1. The square-root process as a transformed Bessel process, the Heston stochastic volatility model, density of volatility.
2. Moments and density of the integral of squared volatility and of the stock price. Fourier and other computational methods.
3. The integral of geometric Brownian motion: first properties, exact and approximate expressions for the density of the integral.
4. Bessel processes and the integral of geometric Brownian motion, Laplace transforms, special properties.

Abstract
The aim of these lectures is to help attendees understand the mathematics related to the integrals (over time) of two diffusions, the square root process and geometric Brownian motion. Both are involved in the analysis of realized variance and in the pricing of volatility derivatives in the stochastic volatility framework.

Speakers
Prof. Roger Nelsen (Clark College, USA) Author of the best-seller An Introduction to Copulas published by Springer Verlag

Title
A course on Copulas

Sessions

1. Basic concepts
2. Archimedean copulas
3. Concordance and its consequences
4. Dependence and stochastic processes

Abstract
Copulas are functions which join or “couple” multivariate distribution functions to their one-dimensional margins. Their importance in statistical modeling is primarily a consequence of Sklar’s theorem: Let H be a two dimensional distribution function with marginal distribution functions F and G. Then there exists a copula such that H(x,y)=C(F(x),G(y)). Conversely, for any distribution functions F and G and any copula, the function H defined above is a two-dimensional distribution function with margins F and G. Thus for the purposes of statistical modeling, it is useful to have a collection of different copulas. In the first two talks, we explore various methods for constructing copulas and their applications. Special attention is given to families of Archimedean copulas and their properties, simulation techniques, and related results.
In statistical modeling, dependence is often of more interest than independence, and many descriptions and measures of dependence are distribution free or scale invariant, and such properties and measures are expressible in terms of copulas. In the third and fourth talks, we discuss copula-based dependence concepts such as concordance, quadrant dependence, likelihood ratio dependence, and tail dependence, and measures of association such as the population versions of Spearman’s rho, Kendall’s tau, and Gini’s gamma. we will also consider the role played by copulas in the study of Markov processes.

Speakers
Prof. Wim Schoutens (Katholieke Universiteit Leuven, Belgica)
Author of the best-seller Levy Processes in Finance: Pricing Financial Derivatives published by Wiley Series in Probability and Statistics

Title
How to use Levy Processes in Finance

Sessions

1. Why do we need Levy ?
2. Levy Models in Equity: the Basics
3. Multivariate Levy Equity Models
4. Levy in Credit Risk

Abstract
This course introduces jump processes in financial modelling. Jumps and extreme events are crucial stylized features and are essential in modelling of the volatile markets. The recent turmoil in the markets have illustrated once more the need for more refined models. The delegates will learn how the classical models (driven by Brownian motions, cfr. Black-Scholes settings) can be significantly improved by considering the more flexible class of Lévy processes. By doing this extreme event and jumps are introduced in the models and a more reliable pricing and a better assessment of the risk presents can be made. Besides the setting up of the theoretical framework, many attention will be paid to the practical aspects. We will deal with the basic vanilla pricing and the calibration of the model to given implied vol surfaces, but also illustrate the effect of Levy models on the pricing of complex structured products and the underlying derivatives structures (Basket products, CDOs, CPPIs, CPDOs, …). All the material will be illustrated on market data. The course brings cutting edge research and recent advances in a practical and intuitive way.

Speakers
Prof. William Shaw (Kings College London, UK)

Title
Modern Numerical and Analytical Methods for Computational Finance

Sessions

1. Quantile functions for Monte Carlo simulation
2. Asymptotic Expansions in Option pricing
3. Update on Copula Simulation methods
4. Dependency without copulas

Abstract
This course will review recent developments in numerical and analytical methods for financial modeling. The numerical emphasis will be on the use of non-linear differential equations to define efficient methods for Monte Carlo sampling through the theory of quantile functions. This will be set in a context that allows such simulations to be employed with an arbitrary copula. (If time permits I will also review modern copula simulation methods and an alternative to the use of copulas.) The analytical emphasis will be on the use of asymptotic methods for creating accurate volatility series, and some examples will be given.

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