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Volume 17,     Number 4,     Winter 2009

 

MULTI-FACTOR LÉVY MODELS FOR PRICING
FINANCIAL AND ENERGY DERIVATIVES
ANATOLIY SWISHCHUK

Abstract. We introduce one-factor and multi-factor α-stable Lévy-based models to price financial and energy derivatives. These models include, in particular, as one-factor models, the Lévy-based geometric motion model, the Ornstein-Uhlenbeck [75], the Vasićek [106], the Cox-Ingersoll-Ross [26], the continuous-time GARCH, the Ho-Lee [53], the Hull-White [56] and the Heath-Jarrrow-Morton [49] models, and as multi-factor models, various combinations of the previous models. For example, we introduce new multi-factor models such as the Lévy-based Heston model, Lévy-based SABR/LIBOR market models, and Lévy-based Schwartz-Smith and Schwartz models. Using change of time method for SDEs driven by α-stable Lévy processes we present the solutions of these equations in simple and compact forms (Propositions 1 and 2). We apply this method to price many financial and energy derivatives such as variance swaps, options, forward and futures contracts.

 

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