Summary: Monte Carlo simulation provides a simple procedure to price securities numerically; however, it does not immediately yield the weights necessary to construct a replicating portfolio. The procedure commonly used consists in approximating the derivatives by perturbing the price of the underlying. Here we suggest an alternative procedure that exploits the semimartingale representation of the dynamics of any redundant security and consists in retrieving the volatility term of that representation. Compared to the alternative procedure, the method we suggest has the advantage that the computational cost is independent of the number of dimensions (unlike the traditional procedure where the cost increases linearly with the number of dimensions).
For the entire collection see [Zbl 1020.00009].