Hedged Monte-Carlo: low variance derivative pricing with objective probabilities
AbstractWe 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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Bibliographic InfoPaper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500031.
Date of creation: Aug 2000
Date of revision:
Publication status: Published in Physica A 289 (3-4) (2001) pp. 517-525.
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-13 (All new papers)
- NEP-CFN-2005-02-13 (Corporate Finance)
- NEP-FIN-2005-02-13 (Finance)
- NEP-RMG-2005-02-13 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Benoit Pochard & Jean-Philippe Bouchaud, 2003. "Option pricing and hedging with minimum expected shortfall," Science & Finance (CFM) working paper archive 500029, Science & Finance, Capital Fund Management.
- Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
- Tompkins, Robert G. & D'Ecclesia, Rita L., 2006. "Unconditional return disturbances: A non-parametric simulation approach," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 287-314, January.
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