Rough volatility models are a class of stochastic volatility models that are based on fractional Brownian motion. In contrast to traditional stochastic volatility models, which assume smooth and continuous paths for the volatility process, rough volatility models assume that the volatility process is rough and exhibits long-range dependence.
The roughness of the volatility process in rough volatility models is controlled by the Hurst parameter, which is related to the degree of persistence or memory in the volatility process. A Hurst parameter value of 0.5 corresponds to Brownian motion, while values greater than 0.5 indicate long-range dependence and increased volatility clustering.
One of the key applications of rough volatility models is in option pricing. Traditional stochastic volatility models assume that the volatility of the underlying asset is constant and can be modeled by a single stochastic process. However, in reality, volatility is not constant and exhibits significant fluctuations over time. Rough volatility models provide a more accurate description of the volatility process and allow for more realistic option pricing.
Rough volatility models can be used to derive option pricing formulas that are more accurate and computationally efficient than traditional models. For example, in the Heston model, which is a popular stochastic volatility model, the volatility process is assumed to follow a specific stochastic differential equation (SDE). In contrast, rough volatility models allow for more flexible and realistic volatility dynamics that are not restricted to a specific SDE.
In addition, rough volatility models can also be used for risk management and hedging strategies. By accurately modeling the volatility process, traders and investors can better manage their risk exposure and develop more effective hedging strategies.
Overall, rough volatility models represent an important development in option pricing and quantitative finance more broadly, as they provide a more accurate and realistic description of financial market dynamics.