The Foresight Bias in Monte-Carlo Pricing of Options with Early
AbstractIn this paper we investigate the so called foresight bias that may appear in the Monte-Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte-Carlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent Monte-Carlo simulations: One simulation is used to estimate the exercise criteria (as a function of some state variable), the other is used to calculate the exercise price based on this exercise criteria. We shall call this the numerical removal of the foresight bias. In this paper we give an exact definition of the foresight bias in closed form and show how to apply an analytical correction for the foresight bias. Our numerical results show that the analytical removal of the foresight bias gives similar results as the standard numerical removal of the foresight bias. The analytical correction allows for a simpler coding and faster pricing, compared to a numerical removal of the foresight bias. Our analysis may also be used as an indication of when to neglect the foresight bias removal altogether. While this is sometimes possible, neglecting foresight bias will break the possibility of parallelization of Monte-Carlo simulation and may be inadequate for Bermudan options with many exercise dates (for which the foresight bias may become a Bermudan option on the Monte-Carlo error) or for portfolios of Bermudan options (for which the foresight bias grows faster than the Monte-Carlo error). In addition to an analytical removal of the foresight bias we derive an analytical correction for the suboptimal exercise due to the uncertainty induced by the Monte-Carlo error. The combined correction for foresight bias (biased high) and suboptimal exercise (biased low) removed the systematic bias even for Monte-Carlo simulations with very small number of paths.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0511002.
Length: 27 pages
Date of creation: 03 Nov 2005
Date of revision: 08 Nov 2005
Note: Type of Document - pdf; pages: 27
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Monte Carlo; Bermudan; Early Exercise; Regression; Least Square Approximation of Conditional Expectation; Least Square Monte Carlo; Longstaff-Schwartz; Perfect Foresight; Foresight Bias;
Find related papers by JEL classification:
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-11-05 (All new papers)
- NEP-CMP-2005-11-05 (Computational Economics)
- NEP-FIN-2005-11-05 (Finance)
- NEP-FMK-2005-11-05 (Financial Markets)
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.:
- Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
- Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
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