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

2000/08/09 by Marc Potters, Jean-Philippe Bouchaud, Dragan Sestovic
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Capital Investment and Risk Analysis #Mathematical Approximation and Integration #Stochastic processes and financial applications #cond-mat

paper · pdf · doi:10.1016/s0378-4371(00)00554-9

published as Physica A 289 (3-4) (2001) pp. 517-525. · LaTeX, 10 pp, 3 eps figures (in text)

arxiv created 2000/08/09 · openalex publication_date 2001/01/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Martingales and stochastic integrals in the theory of continuous trading
• The Pricing of Options and Corporate Liabilities

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