Tid: 22 mars 2011 kl 15.15-17.00.

Föredragshållare: Martin Larsson, School of Operations Research and Information Engineering, Cornell University.

Titel: Discretely sampled variance swaps versus their continuous approximations

Abstract Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify computations. This talk addresses the validity of this approximation. We first give conditions under which the discretely sampled swap values are finite, provided that the continuous approximation has finite value. Surprisingly, for some otherwise reasonable price processes, the discretely sampled swap prices do not exist, thereby invalidating the approximation. Examples are provided. Assuming further that both swap values exist, we study sufficient conditions that guarantee the convergence of the discretely sampled values to their continuous counterparts. Because of its popularity in the literature, we apply our results to the 3/2 stochastic volatility model. Although swap values are always finite in this model, we can prove convergence of the approximation only for some parameter configurations. This suggests that care must be taken when using this model in practice.

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