What does the Bates model include that differentiates it from the Heston model?

• A. Deterministic volatility
• B. Mean-reverting process
• C. Jump process
• D. Constant interest rate

Answer: (C)

The Bates model incorporates a jump process, which adds another layer of complexity to its representation of asset prices compared to the Heston model. The inclusion of a jump process allows the Bates model to capture sudden and significant changes in asset prices, which are often observed in real markets due to events such as earnings announcements, macroeconomic news, or other market shocks. This jump component enables the model to account for higher moments of the return distribution, such as skewness and kurtosis, which are important for accurately pricing options and assessing risk.

On the other hand, the Heston model primarily focuses on stochastic volatility, where volatility itself follows a mean-reverting process but does not include the jump component. This is a critical distinction because the ability to model jumps provides a more realistic approach to asset price movements, particularly in markets that display irregular and sporadic fluctuations. By incorporating jumps into the Bates model, it can provide better fit and predictability for assets that experience abrupt changes.