Monte Carlo Construction of Hedging Strategies against Multi-asset European Claims

For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to nd these magnitudes by Monte Carlo simulation of the corresponding system of stochastic di erential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. We consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarek, Musiela and Jamshidian. 1) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany; 2) Ural State University, Lenin Street 51, 620083 Ekaterinburg, Russia JEL classi cation: E43, G13 AMS Subject Classi cation: 60H30, 65U05, 90A09