USING PARTIAL DIFFERENTIAL EQUATIONS FOR PRICING OF GOODS AND SERVICES
Keywords:partial differential equations, economics, pricing, goods, services
This article is based on the methodology of comparative analysis, using an innovative approach for pricing of various goods and services. Benchmarking is the continuous search to find and adapt better pricing methods that leading to increased profits. We will consider the numerical solution of partial differential equations, based on Black-Scholes model for pricing of goods and services within European option. Also, we will present formulation and numerical behavior of explicit and implicit methods that can be use in pricing for company assets within European option.JEL Codes - Y80
Black, F., and Scholes, M., 1973. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. DOI: http://dx.doi.org/10.1086/260062
Boyle, P. P., and Tian, Y., 1998. An explicit finite difference approach to the pricing of barrier options. Applied Mathematical Finance, 5(1), 17-43. DOI: http://dx.doi.org/10.1080/135048698334718
Brandimarte, P., 2002. Numerical Methods in Finance and Economics: A MATLAB-Based Introduction. Torino, Italy: Politecnico di Torino.
Brennan, M. J., and Schwartz, E. S., 1977. Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion. The Journal of Finance, 32(5), 1699-1715. DOI: http://dx.doi.org/10.1111/j.1540-6261.1977.tb03364.x
Clemen, R. T., and Reilly, T., 1996. Making Hard Decisions: An Introduction to Decision Analysis (2nd ed.). Pacific Grove, CA: Duxbury.
Cvitanic, J., and Zapatero, F., 2004. Introduction to the Economics and Mathematics of Financial Markets. Cambridge, MA: MIT Press.
Elton, E. J., and Gruber, M., 1995. Modern Portfolio Theory and Investment Analysis (5th ed.). New York: John Wiley & Sons.
Fabozzi, F. J., 1996. Bond Markets: Analysis and Strategies. Upper Saddle River, NJ: Prentice Hall.
Figlewski, S., and Gao, B., 1999. The adaptive mesh model: A new approach to efficient option pricing. Journal of Financial Economics, 53(3), 313-351. DOI: http://dx.doi.org/10.1016/S0304- 405X(99)00024-0
Hull, J., 2003. Options, Futures and Other Derivatives (5th ed.). Upper Saddle River, NJ: Prentice Hall.
Hull, J. C., and White, A. D., 1993. Efficient Procedures for Valuing European and American Path- Dependent Options. Journal of Derivatives, 1(1), 21-31. DOI: http://dx.doi.org/10.3905/jod.1993.407869
Kaas, R., Goovaerts, M., Dhaene, J., and Denuit, M., 2008. Modern Actuarial Risk Theory. Using R (2nd ed.). Berlin: Springer-Verlag.
Kemna, A. G. Z., and Vorst, A. C. F., 1990. A pricing method for options based on average values. Journal of Banking & Finance, 14(1), 113-129. DOI: http://dx.doi.org/10.1016/0378- 4266(90)90039-5
Kunitomo, N., and Ikeda, M., 1992. Pricing options with curved boundaries. Mathematical Finance, 2(4), 275-298. DOI: http://dx.doi.org/10.1111/j.1467-9965.1992.tb00033.x
Merton, R. C., 1973. Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141-183. DOI: http://dx.doi.org/10.2307/3003143
Neftci, S. N., 2000. An Introduction to the Mathematics of Financial Derivatives (2nd ed.). San Diego, CA: Academic Press.
Pliska, S. R., 1997. Introduction to Mathematical Finance: Discrete Time Models. Malden, MA: Blackwell Publishers.
Rich, D., 1996. The valuation and behavior of Black-Scholes options subject to intertemporal default risk. Review of Derivatives Research, 1(1), 25-59. DOI: http://dx.doi.org/10.1007/BF01536394
Saaty, T., 1994. Fundamentals of Decision Making. Pittsburg: RWS Publications.
Taleb, N., 1996. Dynamic Hedging: Managing Vanilla and Exotic Options. New York: Wiley.
Tavella, D., and Randall, C., 2000. Pricing Financial Instruments: The Finite Difference Method. New York: Wiley.
Topper, J., 2005. Financial Engineering with Finite Elements. New York: Wiley.
Wilmott, P., 1999. Derivatives: The Theory and Practice of Financial Engineering. Chichester, West Sussex: Wiley.
Wilmott, P., Dewynne, J., and Howison, S., 1993. Option Pricing: Mathematical Models and Computation. Oxford: Oxford Financial Press.
Zvan, R., Forsyth, P., and Vetzal, K., 1997. Robust Numerical Methods for PDE Models of Asian Options. Journal of Computational Finance, 1(2), 39-78. DOI: http://dx.doi.org/10.21314/JCF.1997.006
Zvan, R., Vetzal, K. R., and Forsyth, P. A., 2000. PDE Methods for Pricing Barrier Options. Journal of Economic Dynamics and Control, 24(11-12), 1563-1590. DOI: http://dx.doi.org/10.1016/S0165-1889(00)00002-6
How to Cite
Copyright (c) 2016 SCIENTIFIC ANNALS OF ECONOMICS AND BUSINESS
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All accepted papers are published on an Open Access basis.
The Open Access License is based on the Creative Commons license.
The non-commercial use of the article will be governed by the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License as currently displayed on https://creativecommons.org/licenses/by-nc-nd/4.0
Under the Creative Commons Attribution-NonCommercial-NoDerivatives license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions:
1. they must attribute the contribution in the manner specified by the author or licensor,
2. they may not use this contribution for commercial purposes,
3. they may not alter, transform, or build upon this work.