Leon von Essen: Smooth and Stable Greeks for Autocallables
Frankfurt, Vortrag zur Masterarbeit
- Sondertermin am Mittwoch -
Abstract: We develop a new Monte-Carlo-Estimator for the pricing of certain structured financial derivatives called worst-of Autocallables with an arbitrary number of underlyings. The method combines pathwise and importance sampling elements to develop the first stable estimator for Greeks of higher order. To achieve this, we describe the abstraction of the 2-dimensional bisector into higher dimensions for cones and develop a Gram-Schmidt-type rotation to extend earlier works on the stable calculation of first order finite differences of worst-of Autocallables. Further, we develop a sampling method that is capable of generating unbiased samples from the complement of a cone in the n-dimensional Gaussian plane in smooth dependence to initial parameters. This extends finite differences and pathwise Monte Carlo methods to derivatives of any order. Further, we introduce a payoff-modification that is able to handle non-Lipschitz payoffs, a previous requirement. We show convergence of the new method.
