Wednesday 6 November 2013 h. 14:30, room 2BC30

Stefano Pagliarani (Dip. Mat. - Padova)

"Option pricing in a defaultable model: a characteristic function approach"

Abstract

We consider a defaultable stock (i.e. a financial risky asset) whose predefault dynamics follows a stochastic differential equation driven by a Levy process. Under suitable assumptions on the default time, the price of a contingent claim (i.e. a financial derivative) is obtained in terms of the characteristic function (i.e. the Fourier transform) of the terminal log price. We characterize it as the solution of a complex valued infinite dimensional system of first order ordinary differential equations, which can be seen as an ordinary differential equation in a suitably chosen Banach space. By using this, we provide an explicit eigenfunction expansion for the characteristic function and use it to price contingent claims by means of standard Fourier inversion techniques. Finally, we present numerical results to demonstrate accuracy and efficiency of the method.

Rif. int. C. Marastoni, T. Vargiolu