  We propose a new `hedged' Monte-Carlo (HMC) method to price financial
derivatives, which allows to determine simultaneously the optimal hedge. The
inclusion of the optimal hedging strategy allows one to reduce the financial
risk associated with option trading, and for the very same reason reduces
considerably the variance of our HMC scheme as compared to previous methods.
The explicit accounting of the hedging cost naturally converts the objective
probability into the `risk-neutral' one. This allows a consistent use of purely
historical time series to price derivatives and obtain their residual risk. The
method can be used to price a large class of exotic options, including those
with path dependent and early exercise features.
