Fractional Brownian markets with time-varying volatility and high-frequency data

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 p...

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Bibliographic Details
Published in:Econometrics and statistics 2020-10, Vol.16, p.91-107
Main Authors: Lahiri, Ananya, Sen, Rituparna
Format: Article
Language:English
Subjects:
Asymptotic normality
Fractional Black–Scholes model
Malliavin calculus
Option price
Volatility
Wick financing
Wick Ito Skorohod integration
Wiener chaos
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Summary: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.
ISSN:2452-3062
2452-3062
DOI:10.1016/j.ecosta.2018.10.004