Learning, Pricing, Timing and Hedging of the Option to Invest for Perpetual Cash Flows with Idiosyncratic Risk

39 Pages Posted: 24 Sep 2013 Last revised: 23 Jan 2014

See all articles by Dandan Song

Dandan Song

Hunan University - School of Finance and Statistics

Huamao Wang

University of Kent - Kent Business School

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Date Written: September 23, 2013

Abstract

The paper considers the option of an investor to invest in a project that generates perpetual cash flows, of which the drift parameter is unobservable. The investor invests in a liquid financial market to partially hedge cash flow risk and estimation risk. We derive two 3-dimensional non-linear free-boundary PDEs satisfied by the utility-based prices of the option and the cash flows. We provide an approach to measure the information value. A numerical procedure is developed. We show that investors have not only idiosyncratic-risk-induced but also estimation-risk-induced precautionary saving demands. A growth of estimation risk, risk aversion or project risk delays investment, but it is accelerated if the project is more closely correlated with the market. Partial information results in a considerable loss, which reaches the peak value at the exercising time and increases with project risk and estimation risk. The more risk-averse the investor or the weaker the correlation, the larger the loss.

Keywords: Partial information, Hedging, Real options, Precautionary savings, Information value, Non-linear PDEs

JEL Classification: C61, G11, G31

Suggested Citation

Song, Dandan and Wang, Huamao and Yang, Zhaojun, Learning, Pricing, Timing and Hedging of the Option to Invest for Perpetual Cash Flows with Idiosyncratic Risk (September 23, 2013). Available at SSRN: https://ssrn.com/abstract=2329459 or http://dx.doi.org/10.2139/ssrn.2329459

Dandan Song

Hunan University - School of Finance and Statistics ( email )

School of Finance and Statistics
Changsha, CA 410079
China

Huamao Wang

University of Kent - Kent Business School ( email )

Sibson Building
Canterbury, Kent CT2 7FS
United Kingdom

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
112
Abstract Views
1,043
rank
332,962
PlumX Metrics