Which model is characterized by a mean-reverting stochastic process for volatility?

• A. Black-Scholes model
• B. Heston model
• C. Modern portfolio theory
• D. Bates model

Answer: (B)

The Heston model is characterized by a mean-reverting stochastic process for volatility, making it an essential tool in financial modeling, particularly for options pricing. In this model, the volatility of the underlying asset is not constant but is described by a stochastic process that exhibits mean reversion. This means that volatility tends to return to a long-term average over time, which closely aligns with observed market behavior, especially during periods of market stress where high volatility tends to diminish back toward an average level.

The mean-reverting characteristic of the Heston model allows for a more realistic depiction of the dynamics of volatility compared to models that assume constant volatility, such as the Black-Scholes model. In Black-Scholes, volatility is treated as a fixed parameter, which simplifies calculations but may not capture the actual behavior observed in the market.

The Bates model builds on the Heston framework by incorporating jumps into the asset price process, but it is the Heston model itself that distinctly features the mean-reverting stochastic process solely related to volatility. Modern portfolio theory, on the other hand, focuses on asset allocation and risk-return trade-offs and does not address the stochastic modeling of volatility.

Thus, the Heston model is the correct choice for its unique approach to capturing the time-dependent and