Investment timing under hybrid stochastic and local volatility

• The effects of hybrid stochastic volatility on real option prices are studied.
• The stochastic volatility consists of a fast mean-reverting component and a CEV type one.
• A fast mean-reverting factor lowers real option prices and investment thresholds.
• The increase of elasticity raises real option prices and investment thresholds.
• The effects of the addition of a slowly varying factor depend upon the project value.

We consider an investment timing problem under a real option model where the instantaneous volatility of the project value is given by a combination of a hidden stochastic process and the project value itself. The stochastic volatility part is given by a function of a fast mean-reverting process as well as a slowly varying process and the local volatility part is a power (the elasticity parameter) of the project value itself. The elasticity parameter controls directly the correlation between the project value and the volatility. Knowing that the project value represents the market price of a real asset in many applications and the value of the elasticity parameter depends on the asset, the elasticity parameter should be treated with caution for investment decision problems. Based on the hybrid structure of volatility, we investigate the simultaneous impact of the elasticity and the stochastic volatility on the real option value as well as the investment threshold.