Mathematical Finance Seminar

February 7, 2002 5:30 PM to 7:00 PM

Andrew Lesniewski, BNP Paribas

Swaption Smiles via the WKB Method

We study a three-parameter stochastic volatility model, originally proposed by P. Hagan, for the forward swap rate. The model is essentially a stochasticied version of the CEV model, where the volatility parameter is itself a stochastic process. We construct a computationally efficient, asymptotic solution to this model. This solution allows one to fit a variety of shapes of the volatility smiles in the swaption markets. The technique used to obtain this solution is a WKB expansion around geodesic motion on a suitable hyperbolic manifold.