The Pricing and Timing of the Option to Invest for Cash Flows with Partial Information

21 Pages Posted: 5 Jan 2011 Last revised: 20 Jan 2011

See all articles by Zhaojun Yang

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Dandan Song

Hunan University - School of Finance and Statistics

Jinqiang Yang

affiliation not provided to SSRN

Date Written: January 3, 2011

Abstract

This paper extends real options theory to consider the situation where the mean appreciation rate of cash flows generated by an irreversible investment project is not observable and governed by an Ornstein-Uhlenbeck process. Our main purpose is to analyze the impact of the uncertainty of the mean appreciation rate on the pricing and investment timing of the option to invest under incomplete markets with partial information. We assume that an investor aims to maximize expected discounted utility of lifetime consumption. Based on consumption utility indifference pricing method, stochastic control and filtering theory, under CARA utility, we derive the implied value of cash flows after investment, and then obtain the implied value and the optimal investment threshold of the option to invest, which are determined by a semi-closed-form solution of a free-boundary PDE problem. We show that the solutions are independent of the utility time-discount rate. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations show that partial information leads to a significant loss of the implied value of the option to invest. This loss increases with the uncertainty of the mean appreciation rate. In contrast to standard real options theory, a high volatility of cash flows decreases the implied value of the option to invest as well as the implied information value.

Keywords: Partial information, Cash flows, Consumption utility-based indifference pricing, Real options, Implied information value

JEL Classification: C61, G11, G31

Suggested Citation

Yang, Zhaojun and Song, Dandan and Yang, Jinqiang, The Pricing and Timing of the Option to Invest for Cash Flows with Partial Information (January 3, 2011). Available at SSRN: https://ssrn.com/abstract=1734302 or http://dx.doi.org/10.2139/ssrn.1734302

Zhaojun Yang (Contact Author)

Southern University of Science and Technology - Department of Finance ( email )

No 1088, Xueyuan Rd.
District of Nanshan
Shenzhen, Guangdong 518055
China

HOME PAGE: http://faculty.sustc.edu.cn/profiles/yangzj

Dandan Song

Hunan University - School of Finance and Statistics ( email )

School of Finance and Statistics
Changsha, CA 410079
China

Jinqiang Yang

affiliation not provided to SSRN ( email )

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