AUTHORS: Ladislav Lukáš

Download as PDF

ABSTRACT: The paper is focused on numerical approximation of early exercise boundary within American put option pricing problem. Assuming non-dividend paying, American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. However, the integral equation is known for determination of early exercise boundary. We propose an iterative procedure for numerical solution of that integral equation. We discuss the construction of initial approximations, and we also describe the steps of our submitted procedure in details. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by the sw Mathematica, version 11.1.

KEYWORDS: American put option, early exercise premium, early exercise boundary, pricing problem, integral equation, numerical method

REFERENCES:

[1] AitSahlia, F., and Lai, T. L., A canonical optimal stopping problem for American options and its numerical solution, Names of the Authors, Title of the Paper, Journal of Computational Finance, Vol.3, No.2, 1999, pp. 33-52.

[2] AitSahlia, F., and Lai, T. L., Exercise boundaries and efficient approximations to American option prices and hedge parameters, Journal of Computational Finance, Vol.4, No.4, 2001, pp. 87-103.

[3] Doffou, A., Estimating the early exercise premium of American put index option, Int. Journal of Banking and Finance, Vol.6, No. 1, 2008, pp.31-47.

[4] Dueker, M., Directly Measuring Early Exercise Premiums Using American and European S&P 500 Index Option, Working Paper Series, online, https://research.stlouisfed.org/wp/2002/2002- 016.pdf.

[5] Fries, Ch., Mathematical Finance – theory, modeling, implementation, John Wiley & Sons, Hoboken, New Jersey, 2007.

[6] Jiang, L., Mathematical Modeling and Methods of Option Pricing, World Scientific Publ. Co., Singapore, 2005.

[7] Lukáš, L., American Option Pricing Problem Formulated as Variational Inequality Problem, In: Conf. Proc., 34-th Int. Conf. Math. Methods in Economics 2016, Tech. Univ. of Liberec, Liberec, Czech Republic, 2016, pp.512-517.

[8] Mallier, R., Evaluating approximations to the optimal exercise boundary for American options, Journal of Applied Mathematics, Vol.2, No.2, 2002, pp. 71-92. Hindawi Publishing Corporation, on-line, http://dx.doi.org/10.1155/S1110757X02000268

[9] Neftci, S. N., An Introduction to the Mathematics of Financial Derivatives, 2.ed.,Academic Press, London, 2000.

[10] Pironneau, O., and Achdou, Y., Partial Differential Equations for Option Pricing, In: Mathematical Modeling and Numerical Methods in Finance, Special Volume (Bensoussan, A., and Zhang, Q., eds) of Handbook of Numerical Analysis, Vol.XV, (Ciarlet, P. G., ed), North-Holland, Elsevier, Amsterdam, 2007.

[11] Stamicar, R., Ševčovič, D., and Chadam, J., The early exercise boundary for the American put near empiry: numerical approximation, Canadian Applied Math. Quarterly, Vol.7, No.4, 1999, pp. 427-444.

WSEAS Transactions on Business and Economics, ISSN / E-ISSN: 1109-9526 / 2224-2899, Volume 14, 2017, Art. #26, pp. 235-243


Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0