Derivatives Pricing Based on Stochastic Control With Transaction Cost, Taxes and Dividends

Jianhui YANG, Weikang HE

Abstract


This paper attempts to apply stochastic control theory, considering option pricing on the situation when payment, tax and transaction costs exist, and finally obtain an interval of price, which not only make it more similar to the reality, but also provide reference for investors to make investment decisions. Our paper improved the uncertain volatility model. Based on the theory of stochastic control, we find the viscous solution of nonlinear partial differential equations by numerical methods when transaction cost and tax exist, and complete the empirical analysis on the actual data of the market, which has proved the value of this model.


Keywords


Derivative pricing; UMV model; Stochastic control; Transaction cost; Tax

References


Avellaneda, P. L. (1995). Pricing and hedging derivative securities: In Market with uncertain volalities. Applied Mathematical Finance, 2(2).

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, (81).

Chu, F. (1996). Volatility estimation for stock index options: A garch approach. The Quarterly Review of Economics and Finance, 36(4), 431-450.

Du, Y. L. (2011). Option pricing model based on stochastic optimal control. Statistics and Decision,

Leland, H. E. (1985). Hayne Leland option pricing and replication with transaction costs. The Journal of Financ, 40(5), 1283-1301.

Heston, S. (1993). A closed-form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies, (6).

Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2), 327-343.

Hodges, S. D., & Neuberger, A. (1989). Optimal replication of contingent claims under transaction costs. Review of Futures Markets, 8, 222-239.

Hoggard, T., Whalley, A. E., & Wilmott, P. (1994). Hedging option portfolios in the presence of transaction costs. Advances in Futures and Options Research, 7, 21-35.

Hull, J. C., & White, A. (1987). The pricing of optionson assets with stochastic volatilities. Journal of Finance, 42(2), 281-300.

Shreve. (2003). Stochastic calculus for finance. Berlin: Springer.

Stein, E., & Stein J. (1991). Stock price distributions with stochastic volatility. Review of Financial Studies, 4(4), 727-752.

Whalley, A. E., & Wilmott, P. (1993). Counting the costs. RISK, 6, 59-66.

Whalley, A. E., & Wilmott, P. (1997). An asymptotic analysis of an optimal hedging model for option pricing with transaction costs. Mathematical Finance, 7(3), 307-324.

Wilmott, P. (2004). Paul Wilmott on quantitative finance. Chichester: John Wiley & Sons Ltd.

Yong, J., & Zhou, X. Y. (1999). Stochastic controls: Hamilton systems and Hamilton-Jacobi-Bellman equations. New York: Springer-Verlag.

Zhang, K., & Wang, S. (2009). A computational scheme for uncertain volatility model in option pricing. Applied Numerical Mathematics, 59(8), 1754-1767.




DOI: http://dx.doi.org/10.3968/n

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Jianhui YANG, Weikang HE

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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 three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
[email protected]; [email protected]; [email protected]

 Articles published in Management Science and Engineering are licensed under Creative Commons Attribution 4.0 (CC-BY).

 MANAGEMENT SCIENCE AND ENGINEERING Editorial Office

Address:1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138
Http://www.cscanada.net Http://www.cscanada.org

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures