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We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt,Zt, t… Click to show full abstract
We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt,Zt, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log Sn (or log |Sn| in case Sn is negative) are obtained as n → ∞ under different discretization schemes for the asset price process St and the volatility process σt. Numerical simulations are presented to compare the convergence speeds in different schemes.
Journal Title: Frontiers of Mathematics in China
Year Published: 2018
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