Valuing real options with endogenous payoff

Abstract

This study investigates irreversible investment decisions when the exercise payoff is scale-dependent; thus, it is endogenously determined by the firm's risk management. We find that the scale-dependency gives rise to a speculative risk management strategy: a positive relationship between the firm's derivatives position and unhedged cash flow. Moreover, investment can be hastened or delayed as the underlying uncertainty increases depending on the economic conditions due to the speculative strategy. The main force driving these results, different from those known in the existing literature, is that the firm's risk management is designed to optimize the risk-return trade-off of the endogenous payoff.

Keywords:

• Real options
• Endogenous payoff
• Scale-dependency
• Risk management
• Speculative usage of derivatives
• Risk-return trade-off

JEL classification:

• G11
• G31
• G32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

† There are models in which the investment cost is given as a stochastic process. However, the cost is still an exogenous variable unaffected by a firm's decision.

† We first focus on the case in which the insurance asset exists and is perfectly correlated with the underlying process of the real option, and then extend the model to more general cases: (i) the case in which no such asset exists and (ii) the case in which the correlation is imperfect.

† For example, when a dam is built, the maximum capacity for electricity generation is set.

‡ This example is an extension of the example suggested by Miao and Wang (2007).

† The positive (negative) sign of ${\sigma }_s$ implies that the insurance asset price moves toward the same (opposite) direction as the underlying process moves.

† Note that ξ satisfying (14(14) $({\alpha }_x+r-\theta {\sigma }_x-{\sigma }_x^2)\xi -\frac{1}{2}(\theta +{\sigma }_x{)}^2\frac{\xi }{\xi -1}-(r+\lambda )=0.$(14) ) can be considered as a function of given model parameters such as ${\sigma }_x$, ${\alpha }_x$, λ, and r. Although the arguments of ξ are omitted for simplicity, it is important to take into account the impact of parameters on ξ when we analyze the impact of parameters on the risk management strategy and the optimal exercise strategy in Section 4.

† Note that, for this case, assumption (12(12) $\begin{array}{rl}\theta & >-{\sigma }_x,\text{and}\end{array}$(12) ) is not utilized but induced by applying assumption (13(13) $\begin{array}{rl}{\alpha }_x& >\lambda .\end{array}$(13) ) to equation (A1(A1) $\frac{1}{2}{\theta }^2+(\frac{1}{2}{\sigma }_x-\frac{r+{\alpha }_x}{{\sigma }_x})\theta -(r+\lambda )=0,$(A1) ).

Additional information

Funding

Minsuk Kwak acknowledges that this work was supported by Hankuk University of Foreign Studies Research Fund of 2022. Minsuk Kwak also acknowledges that this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1F1A1062885).