On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis

• Time-changed Lévy processes are used to model the underlying index price.
• The stock index return is driven by three distinct sources of stochastic volatility.
• All three sources of stochastic volatility are needed for index option pricing.
• A negative risk premium is attributed to both diffusion and downside jump volatility.
• A positive risk premium generated by upside jump volatility is uncovered.

This paper investigates the performance of time-changed Lévy processes with distinct sources of return volatility variation for modeling cross-sectional option prices on the CAC40 index during the subprime crisis. Specifically, we propose a multi-factor stochastic volatility model: one factor captures the diffusion component dynamics and two factors capture positive and negative jump variations. In-sample and out-of-sample tests show that our full-fledged model significantly outperforms nested lower-dimensional specifications. We find that all three sources of return volatility variation, with different persistence, are needed to properly account for market pricing dynamics across moneyness, maturity and volatility level. Besides, the model estimation reveals negative risk premium for both diffusive volatility and downward jump intensity whereas a positive risk premium is found to be attributed to upward jump intensity.