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

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  • 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.

Suggested Citation

  • Song, Dandan & Wang, Huamao & Yang, Zhaojun, 2014. "Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 1-11.
    • Handle: RePEc:eee:mateco:v:51:y:2014:i:c:p:1-11
    DOI: 10.1016/j.jmateco.2014.02.009
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    References listed on IDEAS

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