Hedged Monte-Carlo: low variance derivative pricing with objective probabilities

Details Hedged Monte-Carlo: low variance derivative pricing with objective probabilities Hedged Monte-Carlo: low variance derivative pricing with objective probabilities

2000-08-09

arxiv.org/abs/cond-mat/0008147v1

Physica A 289 (3-4) (2001) pp. 517-525.

Physics

Condensed Matter

LaTeX, 10 pp, 3 eps figures (in text)

Scientific paper

10.1016/S0378-4371(00)00554-9

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.

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