Numerical construction of a hedging strategy against the European claim.
- Milstein, Grigori .N.
- Schoenmakers, John G. M.
2010 Mathematics Subject Classification
- 60H30 65U05 90A09
- Derivative pricing and hedging, probabilistic representations, weak approximation of solutions of stochastic differential equations, variance reduction
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 find these magnitudes by Monte Carlo simulation of the corresponding system of stochastic differential 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 asset models with an instantaneous saving bond and the Jamshidian LIBOR rate model.
- Stochastics and Stochastics Reports 73 (1-2), under new title: Monte Carlo construction of hedging strategies against European asset claims.