Parallel implementation of fast PDE solvers for adaptive multi-asset option pricing and hedging under Black and Scholes market models and beyond

Description

Multi-asset options are financial derivatives whose prices depend on those of
$d \geq 2$ underlying securities, the latter ranging from stocks to indices of various
types. These options are of interest to banks, hedge funds and other commodity
trading entities, and enter the compositions of more complex structured products,
hedging and risk management strategies. Commonly encountered types of financial
or mathematical significance include basket options (on portfolios of securities),
exchange options (swaptions), extreme options (best/worst of), quanto options (in-
volving foreign exchange rates), geometric and power options. Furthermore, multi-
asset options may be exercised with European or American style.\\
The objective of this project is the development and implementation of parallel Galerkin methods
on sparse grids for pricing multi-asset options in high
dimensions under Black and Scholes markets and beyond.
The parallelization of fast PDE solvers on sparse grids on distributed-memory
architectures in order to solve elliptic and parabolic problems of high dimensions
($d \geq 20$) in reasonable computing times will be addressed first. Dimensionality
reduction will then be investigated in order to establish adaptive pricing algorithms
based on the discrete recalibration of the volatility covariance matrix.

References

N. Hilber, S. Kehtari , Ch. Schwab, C. Winter, Wavelet finite element method for option pricing highdimensional diffusion market models, SAM Report 2010-01
http://www.sam.math.ethz.ch/reports/2010/01

Contacts

Prof. Christoph Schwab
Sohrab Kehtari