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Séance MA4 - Finance I

Jour lundi, le 7 mai 2007
Salle Nancy et Michel-Gaucher
Président Michèle Breton

Présentations

10h30-
10h55
Risk in Energy Portfolios
  Jean-Guy Demers, HEC Montréal, Méthodes quantitatives de gestion, Québec, Canada

Power markets in New-England have progressively been deregulated during the 1990s, allowing each zone to have its own fluctuating spot price. Such prices have a notoriously high volatility, owing to the difficulty of storing electrical energy and the delays needed to adjust generation levels. In this context, the forward contracts have become increasingly popular, as the preferred instrument to manage price risks. Understanding the statistical behavior of such contracts is a problem facing many market players. This presentation will introduce a parsimonious parametric model, and discuss the constrained optimization involved in the parameter estimation. The model will be used to forecast value at risk on arbitrary portfolios of forward contracts, and on various zones. Extensions to include the natural gas and power-relevant oil-based future markets will also be discussed.


10h55-
11h20
Pricing Interest Rate Derivatives under Stochastic Volatility
  Nabil Tahani, Atkinson School of Administrative Studies, York University, Finance, 4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3
Xiaofei Li, School of Administrative Studies, Atkinson Faculty of Liberal and Professional Studies, York University, 4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3

This paper derives semi-closed-form solutions to a variety of interest rate derivative prices. Our approach consists of first deriving the Frobenius series solution to the cross-moments generating function, and then inverting the characteristic function using the Gauss-Laguerre quadrature rule for the corresponding cumulative probabilities. We apply our approach to value options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars. Our approach is found to be both accurate and fast, and it compares favorably with some alternative approaches in the literature.


11h20-
11h45
An Analysis of the True Notional Bond System Applied to the CBOT T-Bond Futures
  Ramzi Ben-Abdallah, HEC Montréal, Méthodes quantitatives de gestion, 3000, chemin de la Côte-Ste-Catherine, Montréal, Québec, Canada, H3T 2A7
Michèle Breton, GERAD et HEC Montréal, Méthodes quantitatives de gestion, 3000, chemin de la Côte-Ste-Catherine, Montréal, Québec, Canada, H3T 2A7
Hatem Ben-Ameur, HEC Montréal, Méthodes quantitatives de gestion, 3000, chemin de la Côte-Ste-Catherine, Montréal, Québec, Canada, H3T 2A7

The aim of this paper is to test the True Notional Bond System proposed by Oviedo (2006) for the pricing of the Chicago Board of Trade Treasury-bond futures under stochastic interest rates. We propose a model that can handle all the delivery rules embedded in the CBOT T-bond futures, interpreted here as an American-style interest rate derivative. Our pricing procedure is a backward numerical algorithm combining Dynamic Programming and approximation by finite elements.


11h45-
12h10
Option Pricing under GARCH Processes by PDE Methods
  Michèle Breton, GERAD et HEC Montréal, Méthodes quantitatives de gestion, 3000, chemin de la Côte-Ste-Catherine, Montréal, Québec, Canada, H3T 2A7
Javier de Frutos, Universidad de Valladolid, Matematica Aplicada y Computacion, Valladolid, Spain, 47011

We present an algorithm to pricing options under GARCH processes. We suppose that the process evolves as a geometric Brownian motion between two consecutive observation dates allowing a partial differential equation formulation of the pricing problem. The procedure is general and, in consequence, it can be applied to a large family of different dynamics specifications. We analyze both European and American style contracts and compare the results with other alternative pricing procedures.


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