Optioned Portfolio Selection: Models and Analysis

25 Pages Posted: 19 Sep 2008

See all articles by Jianfeng Liang

Jianfeng Liang

affiliation not provided to SSRN

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering

Duan Li

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Date Written: 2007-05

Abstract

The mean-variance model of Markowitz and many of its extensions have been playing an instrumental role in guiding the practice of portfolio selection. In this paper we study a mean-variance formulation for the portfolio selection problem involving options. In particular, the portfolio in question contains a stock index and some European style options on the index. A refined mean-variance methodology is adopted in our approach to formulate this problem as multistage stochastic optimization. It turns out that there are two different solution techniques, both lead to explicit solutions of the problem: one is based on stochastic programming and optimality conditions, and the other one is based on stochastic control and dynamic programming. We introduce both techniques, because their strengths are very different so as to suit different possible extensions and refinements of the basic model. Attention is paid to the structure of the optimal payoff function, which is shown to possess rich properties. Further refinements of the model, such as the request that the payoff should be monotonic with respect to the index, are discussed. Throughout the paper, various numerical examples are used to illustrate the underlying concepts.

Suggested Citation

Liang, Jianfeng and Zhang, Shuzhong and Li, Duan, Optioned Portfolio Selection: Models and Analysis (2007-05). Mathematical Finance, Vol. 18, Issue 4, pp. 569-593, October 2008. Available at SSRN: https://ssrn.com/abstract=1270343 or http://dx.doi.org/10.1111/j.1467-9965.2008.00348.x

Jianfeng Liang (Contact Author)

affiliation not provided to SSRN

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering ( email )

Ho Sin Hang Engineering Building, Room 228
Shatin, N.T.
Hong Kong
852 2609 8240 (Phone)
852 2603 5505 (Fax)

HOME PAGE: http://www.se.cuhk.edu.hk/~zhang/

Duan Li

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
(852) 2609-8323 (Phone)
(852) 2609-5505 (Fax)

HOME PAGE: http://www.se.cuhk.edu.hk/~dli/

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