Workshop on
Financial Mathematics
(December 24-25, 2005)

FIRST ANNOUNCEMENT

"Derivatives" as a branch of modern finance continues to be one of the fastest growing areas within the corporate world, accounting for a very significant part of the financial market.

This together with the sophistication and complexity of modern financial products, has acted as the motivation for new mathematical models and the subsequent development of computational schemes. Investment decisions for predicting risk and return are being increasingly based on principles taken from the Mathematical Finance arena, providing a challenge for both academics and practitioners. Consequently, a solid command of the fundamentals and techniques of mathematical finance is essential for a responsible approach to the trading and risk control of complex financial products.

Although relatively young, financial mathematics has developed rapidly into a substantial body of knowledge, and become an established branch of mathematics. The main attractive feature of this subject area is that as an applied mathematical discipline it plays a central role in current developments in its domain of application. It has a reciprocal - relationship with the ‘real world’ while it both draws from and has direct implications upon every-day financial practice in the commercial arena. LUMS will be hosting a two day workshop mathematical finance. Through a series of lectures, the applied aspects of mathematical finance, in particular theoretical and computational techniques for option pricing will be presented, through a combination of standard well known methods, and cutting edge research. Computer lab  will also be arranged.

The workshop will be particularly beneficial to mathematics, economics, computer sciences and business students and should assist in further developing their interest, whilst introducing new students to this exciting branch of mathematical science. In addition academics will find the meeting very interesting, and those keen on introducing mathematical finance in their own institutions as part of their mathematics syllabuses will have an opportunity to discuss this with the workshop presenters, as well as establishing long terms links with them.

Computational PDE Approach in Financial Mathematics

 Abdul Qayyum M. Khaliq
Department of Mathematical Sciences
Middle Tennessee State University, USA

Outline

1. Assets in Financial Markets

• Statistics of asset price motion

• Derivative Securities

2. Black-Scholes Hedging

• Wiener Process

• Itô’s Lemma

• The link between Stochastic Differential Equations and PDEs

• The Black-Scholes PDE

• American Options (Early Exercise features)

3. Numerical Methods for Complex Products

• Exotic Options

• American Options and free boundaries

• Multi- Asset Basket Options

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Theoretical and Computational Methods for
Interest Rate Modelling

Riaz Ahmad
Mathematical & Computational Finance
7City Group, London, UK

Outline 

1. Stochastic interest rate models

• stochastic differential equation for the spot interest rate;

• bond pricing PDE;

• popular models for the spot rate (Vasicek; Cox, Ingersoll, Ross and Hull & White);

• solutions of the bond pricing equation.

• Calibration:  the importance of matching theoretical and market prices; time dependent one factor models (Ho & Lee, extended Vasicek)

2. Monte Carlo Method

• Option pricing: Plain Vanilla’s, Asians, Lookbacks and interest rates.

• Stochastic interest rate option pricing models.

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Portfolio Selection
Raouf Ghomrasni
Institut für Mathematik,
Technische Universität, Germany

Outline

1-  Stochastic Portfolio Theory

1.1 Stocks and Portfolios
1.2 Relative Return and the Market Portfolio
1.3 Portfolio Behavior and Optimization

2-  Stock Market Behavior and Diversity

2.1 The Long-Term Behavior of the Market
2.2 Stock Market Diversity
2.3 Entropy as a Measure of Market Diversity

3-  Functionally Generated Portfolios

3.1 Portfolio Generating Functions
3.2 The No-Arbitrage Hypothesis
3.3 Measure of Diversity

4-  Portfolios of Stock Selected by Rank

4.1 Rank Processes and Local Times
4.2 Portfolios Generated by Functions of Ranked Market Weights
4.3 Examples of Rank-Dependent Portfolios and Applications.

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Workshop Presenters

Abdul Q. M. Khaliq is Professor of Mathematics at Middle Tennessee State University, where he teaches Actuarial and Financial Mathematics. Dr. Khaliq's current area of research is  Computational Finance. He obtained his MSc and PhD in Mathematics from Brunel University, UK. Prof. Khaliq is a guest editor of Special Issue on Numerical PDE Methods in Finance., The Journal of Computational and Applied Mathematics.

Riaz Ahmad is course director at 7city London (a European finance training company) for all mathematical and computational finance based education. He holds a BSc, MSc and PhD in mathematics from King's College London, Imperial College London and University College London, in turn. His research interests are in the theoretical and computational methods for derivative pricing.

Raouf Ghomrasni is at Institute fur Matematik, Technische Universitat Berlin. He holds a M.Sc (University of Paris XII, France) and Ph.D (University of Aarhus, Denmark) in Mathematics. His current research interests are in: Stochastic differential equations, Asian options and Applications of Levy processes in finance.
 

Registration Fee:
University Faculty/Academia Rs. 500, Students Rs. 250, Others Rs. 1000,
Participants from outside Pakistan : US $ 100.

Dead line for registration is Dec. 10, 2005.

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