Pricing European Options by Numerical Replication: Quadratic Programming with Constraints

35 Pages Posted: 1 Nov 2005

See all articles by Valeriy Ryabchenko

Valeriy Ryabchenko

University of Florida

Sergey Sarykalin

University of Florida

Stanislav P. Uryasev

University of Florida

Date Written: September 23, 2005

Abstract

The paper considers a regression approach to pricing European options in an incomplete market. The algorithm replicates an option by a portfolio consisting of the underlying security and a risk-free bond. We apply linear regression framework and quadratic programming with linear constraints (input = sample paths of underlying security; output = table of option prices as a function of time and price of the underlying security). We populate the model with historical prices of the underlying security (possibly massaged to the present volatility) or with Monte Carlo simulated prices. Risk neutral processes or probabilities are not needed in this framework.

Keywords: options pricing, incomplete markets, non-self-financing portfolio, hedging

Suggested Citation

Ryabchenko, Valeriy and Sarykalin, Sergey and Uryasev, Stanislav P., Pricing European Options by Numerical Replication: Quadratic Programming with Constraints (September 23, 2005). Available at SSRN: https://ssrn.com/abstract=801285 or http://dx.doi.org/10.2139/ssrn.801285

Valeriy Ryabchenko

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

Sergey Sarykalin

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-1464 ext.2040 (Phone)

Stanislav P. Uryasev (Contact Author)

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)

HOME PAGE: http://www.ise.ufl.edu/uryasev/

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