Correction to Black-Scholes formula due to fractional stochastic\n volatility

2015/09/03 by Josselin Garnier, Knut Sølna, Garnier, Josselin +1 · 1 citation
Economics, Econometrics and Finance · #60G22 #60H10 #60K37 #91G80 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1509.01175

openalex publication_date 2015/09/03 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Empirical studies show that the volatility may exhibit correlations that\ndecay as a fractional power of the time offset. The paper presents a rigorous\nanalysis for the case when the stationary stochastic volatility model is\nconstructed in terms of a fractional Ornstein Uhlenbeck process to have such\ncorrelations. It is shown how the associated implied volatility has a term\nstructure that is a function of maturity to a fractional power.\n

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• Small-time asymptotics for Gaussian self-similar stochastic volatility models
• Testing for jumps in a discretely observed process
• Asymptotic behaviour of the fractional Heston model
• Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

Cited by

• Path-integrals and optimal paths for the fractional Ornstein-Uhlenbeck process

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