Advances in Natural Science
Option Pricing Model With Continuous Dividends
Abstract
This paper discusses the problem of pricing on European options in jump-diffusion model by martingale method. We assuming jump process are more commen then Possion process a kind of nonexplosive counting process. Supposing that the dividend for each share of the security is paid continuously in time at a rate equal to a fixed fraction of the price of the security. By changing the basic assumption of R.C.Merton option pricing model to the assumption. It is established that the behavior model of the stock pricing process is jump-diffusion process. With risk-neutral martingale measure, pricing formula and put-call parity for European options with continuous dividends are obtained by stochastic analysis method. The results of Margrabe are generalized.
Keywords
Full Text:
PDFReferences
Angelo, L. (2009). Successive quadratic programming: Decomposition methods. Encyclopedia of Optimization, 7, 3866-3871.
Ball, C., & Roma, A. (1993). A jump diffusion model for the European monetary system. Journal of International Money and Finance, 12(6), 475-492.
Black, F., & Scholes, M . (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(1), 637-654 .
Cai, W. K., & Mao, J. J. (2002). Polyhedron on quadratic programming and the simplex algorithm. Journal of Shanghai Electric Power, 18(2), 55-58.
Duffie, D. (1996). Dynamic asset pricing theory (2nd ed.). New Jersay: Princeton University Press.
Follmer, H., & Leukert, P. (2000). Efficient hedging:cost versus shortfall risk. Finance and Stochastics, 4(2), 117-146.
Gill, P. E., & Wong, E. (2011). Sequential Quadratic Programming Methods. The IMA Volumes in Mathematics and Its Applications, 154, 147-224.
Harold, J., & Kushner. (2000). Jump-Diffusions with Controlled Jumps: Existence and Numerical Methods. Journal of Mathematical Analysis and Applications, 249(1), 179-198.
Jeanblanc, M., & Pontier, M. (1990). Optimal portfolio for a small investor in a market model with discontinuous prices. Applied Mathematical Optimization, 22(3), 287-310.
Kou, S. S. (2001). Algorithm for finding all solutions of lcp-integer sets method. Journal of Tianjin University, 34(5), 582-593.
Merton, R. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economics Theory, 3(4), 373-413.
Merton, R. C. (1976). Option pricing when underlying stock return are discontinuous. Journal of Economics, 36(3), 125-144 .
Nakano, Y. (2004). Minimization of shortfall risk in a jump-diusion model. Statistics & Probability Letters, 67(1), 87-95.
Pham, H. (2000). Dynami Lp- hedging in discrete time under cone constraints. SIAM J.control Optim, 38(3), 665-682.
Rieger, M. O. (2012). Optimal financial investments for non-concave utilityfunctions. Economics Letters, 114(3), 239-240.
Samuelson, P. A., & Merton, R. C. (1969). A complete model of warrant pricing that maximizes utility. Indust.Manag. Rev., 10, 17-46.
Yang,Y. F., Zhang, S. G., & Xia, X, G. (2013). Option pricing model with stochastic exercise price. Progress in Applied Mathematics, 5(1), 22-31.
Yang, Y. F., & Hao, J. (2013). Wealth optimization models with stochastic volatility and continuous dividends. International Business and Management, 6(1), 51-54.
Yang, M. S., & Luo, C. T. (2006). The optimization principle, method and solving software. Beijing: Science Press.
Yuan, Y. X. (2008). Nonlinear optimization method. Beijing: Science Press.
DOI: http://dx.doi.org/10.3968/%25x
DOI (PDF): http://dx.doi.org/10.3968/%25x
Refbacks
- There are currently no refbacks.
Copyright (c) 2015
Share us to: 
Reminder
How to do online submission to another Journal?
If you have already registered in Journal A, then how can you submit another article to Journal B? It takes two steps to make it happen:
1. Register yourself in Journal B as an Author
Find the journal you want to submit to in CATEGORIES, click on “VIEW JOURNAL”, “Online Submissions”, “GO TO LOGIN” and “Edit My Profile”. Check “Author” on the “Edit Profile” page, then “Save”.
2. Submission
Go to “User Home”, and click on “Author” under the name of Journal B. You may start a New Submission by clicking on “CLICK HERE”.
We only use the following emails to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
[email protected]; [email protected]; [email protected]
[email protected];[email protected]
Articles published in Advances in Natural Science are licensed under Creative Commons Attribution 4.0 (CC-BY).
ADVANCES IN NATURAL SCIENCE Editorial Office
Address: 1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.
Telephone: 1-514-558 6138
Website: Http://www.cscanada.net; Http://www.cscanada.org
E-mail:[email protected]; [email protected]
Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures 
