University of Illinois Urbana-Champaign
Short maturity Asian option pricing and large deviation principle
ABSTRACT: Asian options are widely traded in the ﬁnancial markets, whose payoﬀ at maturity involves the average of historic price of the underlying asset. This path-dependent feature of Asian options prevent any simple closed-form pricing formulas. In this talk we will discuss asymptotic estimates for Asian options with forward starting date and short maturities. We are particularly interested in the case of out-of-the-money, where asymptotic estimate of its price is governed by large deviation, and the corresponding rate function is an interpolation between the European case and the regular Asian case.
In the second half of this talk, we will discuss cases in which the underlying stochastic model is strictly degenerate. It requires a good understanding of small time behaviors of strictly degenerated diﬀusion processes, which has been a long-standing open question. I will present a recent progress in developing a graded large deviation principle for diﬀusions of such kind. Parts of this talk are based on joint work with Fabrice Baudoin and Gerard Ben Arous.