Journées de l'optimisation 2007 Optimizations days

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.

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.

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.

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.