Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk

Song, Dandan; Wang, Huamao; Yang, Zhaojun

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 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. © 2014 Elsevier B.V.

Citation

Song, D., Wang, H., & Yang, Z. (2014). Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk. Journal of Mathematical Economics, 51(1), 1-11. https://doi.org/10.1016/j.jmateco.2014.02.009

• Journal Article Type: Article
• Acceptance Date: Feb 25, 2014
• Online Publication Date: Mar 4, 2014
• Publication Date: 2014-03
• Deposit Date: Apr 7, 2020
• Publicly Available Date: Apr 29, 2020
• Journal: Journal of Mathematical Economics
• Print ISSN: 0304-4068
• Electronic ISSN: 1873-1538
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 1
• Pages: 1-11
• DOI: https://doi.org/10.1016/j.jmateco.2014.02.009
• Public URL: https://nottingham-repository.worktribe.com/output/4267113
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0304406814000378
• Additional Information: This article is maintained by: Elsevier; Article Title: Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk; Journal Title: Journal of Mathematical Economics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jmateco.2014.02.009; Content Type: article; Copyright: Copyright © 2014 Elsevier B.V. All rights reserved.