*Tid:* **22 mars 2011 kl 15.15-17.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25.
Karta!
*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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