Moderate deviations for Euler-Maruyama approximation of Hull-White stochastic volatility model

We consider the Euler-Maruyama discretization of stochastic volatility model dS_t = σ_tS_tdW_t, dσ_t = ωσ_tdZ_t, t ∈ [0, T], which has been widely used in financial practice, where W_t,Z_t, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log S_n (or log |S_n| in case S_n is negative) are obtained as n → ∞ under different discretization schemes for the asset price process S_t and the volatility process σ_t. Numerical simulations are presented to compare the convergence speeds in different schemes.