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

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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.

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Acknowledgements

Hui JIANG was supported by the National Natural Science Foundation of China (Grant No. 11771209) and the China Postdoctoral Science Foundation (Grant No. 2013M531341, 2016T90450); Shaochen WANG was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2017BQ108).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Yunshi Gao & Hui Jiang

  2. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Shaochen Wang

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  1. Yunshi Gao
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  2. Hui Jiang
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  3. Shaochen Wang
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Correspondence to Shaochen Wang.

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Gao, Y., Jiang, H. & Wang, S. Moderate deviations for Euler-Maruyama approximation of Hull-White stochastic volatility model. Front. Math. China 13, 809–832 (2018). https://doi.org/10.1007/s11464-018-0705-0

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  • DOI: https://doi.org/10.1007/s11464-018-0705-0

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