Strategic capacity investment with stochastic volatility in a duopoly market

This study investigates the optimal timing and capacity choices of investment in a duopoly market where the instantaneous variance of demand shock is assumed to follow a Cox–Ingersoll–Ross (CIR) stochastic process. We derive asymptotic expressions for strategic investment problems by applying the asymptotic techniques developed by Fouque et al. (Derivatives in financial markets with stochastic volatility, Cambridge University Press, Cambridge, 2000) and investigate the joint effect of competition and additional uncertainty in the instantaneous variance on the optimal investment triggers and capacity levels of duopoly firms. Within the real options game framework, we obtain the following results: (1) the effects of the mean-reversion speed or the volatility of instantaneous variance on the asymptotic thresholds and capacity levels depend on the sign of correlation between the stochastic demand and its variance process. Meanwhile, both asymptotic thresholds and capacity levels increase with the long-term mean of variance; (2) with an increase in speed of mean reversion, the asymptotic solutions converge to the constant volatility solutions; (3) compared to the sequential game, the first investor under the preemptive game invests earlier with a small capacity to avoid market capture by its competitor.