Real options under a double exponential jump-diffusion model with regime switching and partial information

Abstract

We consider the irreversible investment in a project which generates a cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We provide a method to measure the information value, i.e. the difference between the option values under the two different cases. We present numerical solutions by finite difference methods. By numerical analysis, we find that: (i) the higher the jump intensity, the later the option to invest is exercised, but its effect on the option value is ambiguous; (ii) the option value increases with the belief in a boom economy; (iii) if investors are more uncertain about the economic environment, information is more valuable; (iv) the more likely the transition from boom to recession, the lower the value of the option; (v) the bigger the dispersion of the expected return, the higher the information value; (vi) a higher cash flow volatility induces a lower information value.

Keywords:

• Real options
• Partial information
• Information value
• Double exponential jump-diffusion process

JEL Classification:

• G11
• G13
• C61
• D92

Acknowledgements

An anonymous referee provided helpful suggestions that considerably improved the paper. All errors and omissions are our own.

Notes

No potential conflict of interest was reported by the authors.

1 According to (4(4) $$\begin{array}{c}\hfill Q(x;l)=q(l)x,\end{array}$$(4) ) and (29(29) $$\begin{array}{c}\hfill H(x,\mathit{\pi })=[(1-\mathit{\pi })q_0+\mathit{\pi }{q}_1]x,\end{array}$$(29) ), we similarly derive that the information value after investment is zero. This result explains that information is not valuable any more after the investment is made.

2 A vertical line in the figures throughout this paper specifies an investment threshold.

4 The local truncation errors associated with the approximations given above are $O({\mathrm{\Delta }}_x^2)$ and $O({\mathrm{\Delta }}_{\mathit{\pi }}^2)$.

Additional information

Funding

The research reported in this paper was supported by the National Natural Science Foundation of China [project number 71171078], [project number 71371068], [project number 71202007], [project number 71522008]; Macao Science and Technology Fund [FDCT 025/2016/A1]; New Century Excellent Talents in University [grant number NCET-13-0895]; Innovative Research Team of Shanghai University of Finance and Economics [grant number 2016110241]; Fok Ying-Tong Education Foundation of China [grant number 151086].