An Alternative Formula to Price American Options
AbstractWe give a new way to price American options, using Samuelson´s formula. We first obtain the option price corresponding to a European option at time t, weighting it by the probability that the underlying asset takes the value S at time t. This factor is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can introduce systematically the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamic system in the form of a set of ordinary differential equations we only have to solve a partial differential equation, for the transition probability density. In this context, we verify, for the sake of consistency, that this formula is consistent with the Black-Scholes model.
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Bibliographic InfoPaper provided by Banco de México in its series Working Papers with number 2009-06.
Date of creation: Aug 2009
Date of revision:
American options; Fokker-Planck; Black-Scholes; Samuelson; density probability function.;
Find related papers by JEL classification:
- C00 - Mathematical and Quantitative Methods - - General - - - General
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-05 (All new papers)
- NEP-CFN-2009-09-05 (Corporate Finance)
- NEP-RMG-2009-09-05 (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.:
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- Bladt, Mogens & Rydberg, Tina Hviid, 1998. "An actuarial approach to option pricing under the physical measure and without market assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 65-73, May.
- Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Papers cond-mat/0404103, arXiv.org.
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