Pricing of baskets, Asians and swaptions under affine Lévy models

In this paper we revisit Curran’s (1994) and Rogers’ & Shi’s (1995) lower bounds for the value of an Asian option, and show how to apply it to the valuation of basket options, Asian options and swaptions in a setting where the underlyings are exponentially affine in the state variables, and where we know the characteristic function hereof. Examples of models for which the techniques apply are models where the logarithm of the underlying asset is in the affine Lévy class, which consists of the affine jump-diffusion class, the Lévy market models, and various extensions and mixtures hereof. Numerical results for swaptions and Asians demonstrate that the lower bound is the most accurate approximation considered for these more general models. For swaptions we also come up with an alternative, faster approximation, which is heavily inspired on the Singleton-Umantsev (2002) approximation.

A presentation of this paper at the 5th Winter school on Financial Mathematics can be found here.