13:00
In this seminar, we discuss three questions related to the finite difference computation of early exercise options, one of which has a useful answer, one an interesting one, and one is open.
We begin by showing that a simple iteration of the exercise strategy of a finite difference solution is efficient for practical applications and its convergence can be described very precisely. It is somewhat surprising that the method is largely unknown.
We move on to discuss properties of a so-called penalty method. Here we show by means of numerical experiments and matched asymptotic expansions that the approximation of the value function has a very intricate local structure, which is lost in functional analytic error estimates, which are also derived.
Finally, we describe a gap in the analysis of the grid convergence of finite difference approximations compared to empirical evidence.
This is joint work with Jan Witte and Sam Howison.