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Weak error rates of numerical schemes for rough volatility

2022/03/17 by Paul Gassiat, Gassiat, Paul
Economics, Econometrics and Finance · Social Sciences · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2203.09298

openalex publication_date 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index H ∈ (0,1/2). We obtain results on the rate of convergence for the weak error of such approximations, in the special cases when either the integrand is the fBm itself, or the test function is cubic. Our result states that the convergence is of order (3H+ (1)/(2)) \wedge 1 for exact left-point discretization, and of order H+(1)/(2) for the hybrid scheme with well-chosen weights.

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