A comparative effectiveness of stochastic approximation method and pseudo inversion method for solution to PDE with financial application
Abstract
This paper presents a comparative effectiveness of stochastic approximation method and pseudo inversion method for American option valuation under the Black-Scholes model. The stochastic approximation method and pseudo inversion method base its analysis on a drifted financial derivative system. With finer discretization, space nodes and time nodes, we demonstrate that the drifted financial derivative system can be efficiently and easily solved with high accuracy, by using a stochastic approximation method and pseudo inversion method. The stochastic approximation method proves to be faster in pricing an American options than the pseudo inversion method which needs the system to be stabilized for its accuracy. An illustrative example is given in concrete setting.
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M. Brennan, and E. Schwartz, âThe Valuation of American put Optionsâ, Journal of Finance, vol. 32, pp. 449-462, 1977.
M. Brennan, and E. Schwartz, âFinite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims a Synthesisâ, Journal of Financial and Quantitative Analysis, vol. 13. pp. 461-474, 1978.
E.S. Schwartz, The Valuation of Warrant: Implementing a New Approachâ, Journal of Financial Economics, vol. 4, pp. 79-93, 1977.
P. Jailtet, D. Lamberton, and B. LapeyreâVariational Inequalities and the Pricing of American Optionsâ, Applied Mathematics, vol. 21, pp. 263-289, 1990.
T-L. Horng and C-Y.Tien, âA Simple Numerical Approach for Solving American Option Problemsâ, Proc.Of the World Congress on Engineering, vol. 1.pp. 1-6, 2013.
B.O. Osu and O.U. Solomon, âA stochastic algorithm for the valuation of financial derivatives using the hyperbolic distributional variatesâ, Journal of Mathematical Finance Letters (FML) vol. 1, No. 1. pp. 43-56, 2012.
M. Broadie, and J. DetempleâAmerican Option valuation: New Bounds Approximation, and a Comparison of existing methodsâ, Review of Financial Studies, vol. 9. pp. 1211-1250, 1996.
R. Geske, and K. Shastri, âValuation by Approximation a Comparison of Alternative Option Valuation Techniquesâ, Journal of Financial Quantitative Analysis.Vol. 20, pp. 45-71, 1985.
F. Black, and M. Scholes, âThe Pricing of Options and Corporate Liabilities. âJournal of Political Economy, vol. 81, pp, 637-654, 1973.
R. Merton, âTheory of Rational Option Pricingâ, Bell Journal of Economics and Management Science, vol. 4, pp. 141-183, 1973.
R. White, âNumerical Solution to PDEs with Financial Applicationsâ, Open Gamma Quantitative Research n.10(2013).
M. Shibli, âDynamics and Controllability of Financial derivatives: Towards Stabilization of the Global Financial System Crisisâ. Journal of Mathematical Finance, 2012, 2, pp. 54-65, Doi: 10.4236/jmf. 2012. 21007, (2012).
D. Luca and G. Oriolo, âModeling and Control of Non-holomic Mechanical Systemsâ, In: J.A. Kecskemethy, Ed., Kinematics and Dynamics of Multi-Body Systems, CISM. Courses and lectures, No. 360, Springer-Verlage, pp. 277-342, New York, 1995.
K. Ogata, âModern Control Engineering,â Prentice Hall, Upper Saddle River, 1997.
P. Bjerksund and G. Stensland, âClosed Form Valuation of American Optionsâ, Working Paper NHH. 2002. 23.
B.O. Osu and O.U. Solomon, âA Simple Stochastic Algorithm for Solution to PDE with Financial Applicationâ, Journal of the Nigerian Association of Mathematical Physics, vol. 32, pp. 125-132, Nov. 2015.
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