Fractional Brownian markets with time-varying volatility and high-frequency data
Econometrics and Statistics
Diffusion processes driven by fractional Brownian motion (fBm) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock prices observed in real markets. Option prices for such models under constant drift and volatility are available. Option prices are obtained under time varying volatility. The expression of option price depends on the volatility and the Hurst parameter of the model, in a complicated manner. A central limit theorem is derived for the quadratic variation as an estimator for volatility for both the cases, constant as well as time varying volatility. The estimator of volatility is useful for finding estimators of option prices and their asymptotic distributions.
Lahiri, Ananya and Sen, Rituparna, "Fractional Brownian markets with time-varying volatility and high-frequency data" (2020). ISI Best Publications. 43.