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Comité de coordination


Financial Mathematics / Mathématiques financières
(Luis Seco, Organizer)

Scenario generation techniques in mark-to-future analysis

The fundamental conceptual difficulty in mark-to-future is the ability to generate scenarios that mimic reality. The challenge, even in the static case, is to capture multidimensional distributions with very limited amount of historical information.

In this paper, we overview existing as well as new methodologies in the generic area of scenarion generation, and introduce a collection of benchmarks to evaluate the accuracy of each technique. Finally, we apply our methodology to a number of business cases.

TOM HURD, McMaster
Estimation of multivariate Levy distributions

Since the pioneering work of Mandelbrot and Fama in the early 1960s, evidence has accumulated that many financial indices follow Levy (or stable) distributions, which arise naturally as the limiting distributions of large aggregations of variates with Pareto (or power law) distributions. Recent research on self-organizing criticality (a proposed generator for Pareto laws) has rekindled interest on the ubiquity of Pareto laws in financial data.

Although the problem of estimating univariate Levy distributions has been well-studied, little is known about estimating multivariate distributions. Unlike the Gaussian case, the multivariate Levy case is not a simple generalization of the univariate case. Multivariate Levy distributions exhibit a rich and subtle dependence structure, which, strongly influences the distribution of extreme events. Accurately estimating this dependence structure (and understanding its consequences) is therefore critical for multifactor risk management in a Levy regime.

We have developed methods to estimate multivariate Levy distributions from empirical data. Once the distribution is known, methods of multifactor portfolio optimization can be used to manage risk. This methodology is used to produce software to simulate multivariate Levy data; a known distribution can be used to generate synthetic scenarios with which to stress-test risk-management strategies. They would also provide a framework for mark-to-future analysis.

ALI LARI-LAVASSANI, University of Calgary, Calgary, Alberta  T2N 1N4
Modeling and valuing energy derivatives

Energy markets and specially electricity markets are a lot more complex than equity or interest rate or foreign exchange markets. I will discuss some issues regarding the modeling of the underlying price processes, their applications to some exotic energy derivatives and their numerical implementations.

TOM SALISBURY, York University
Knockout baskets and survivorship bias

I will describe some joint work with Moshe Milevsky and Scott Warlow, concerning the pricing of stock baskets. These baskets have knockout provisions, so that stocks may be thrown out of the basket depending on their performance relative to other components of the basket. The mathematical tools involved include conditioned Brownian motion. The financial motivation is the quantification of survivorship bias.


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