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Article Dans Une Revue SIAM Journal on Financial Mathematics Année : 2023

Weak error rates of numerical schemes for rough volatility

Résumé

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 $H \in (0,1/2)$. 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 $(3H+ \frac{1}{2}) \wedge 1$ for exact left-point discretization, and of order $H+\frac{1}{2}$ for the hybrid scheme with well-chosen weights.

Dates et versions

hal-03867148 , version 1 (23-11-2022)

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Citer

Paul Gassiat. Weak error rates of numerical schemes for rough volatility. SIAM Journal on Financial Mathematics, 2023, 14 (2), pp.475-496. ⟨10.1137/22M1485760⟩. ⟨hal-03867148⟩
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