Hedged Monte-Carlo: low variance derivative pricing with objective probabilities
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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|Date of creation:||Aug 2000|
|Date of revision:|
|Publication status:||Published in Physica A 289 (3-4) (2001) pp. 517-525.|
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- Andrew Matacz & Jean-Philippe Bouchaud, 1999. "An empirical investigation of the forward interest rate term structure," Science & Finance (CFM) working paper archive 500047, Science & Finance, Capital Fund Management.
- Farhat Selmi & Jean-Philippe Bouchaud, 2000. "Hedging large risks reduces the transaction costs," Science & Finance (CFM) working paper archive 500033, Science & Finance, Capital Fund Management.
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