TY - JOUR
T1 - Convergence analysis for continuous-time Markov chain approximation of stochastic local volatility models
T2 - Option pricing and Greeks
AU - Ma, Jingtang
AU - Yang, Wensheng
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/4
Y1 - 2022/4
N2 - This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options under the general framework of stochastic local volatility (SLV) models. The stochastic local volatility models studied in this paper include Heston model, 4/2 model, α-Hypergeometric model, stochastic alpha beta rho (SABR) model, Heston-SABR model and quadratic SLV model. Using the stochastic flow theorem, the closed-form CTMC approximation formula for the Greeks are obtained and the second order convergence rates are proved. Numerical examples confirm the theoretical findings.
AB - This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options under the general framework of stochastic local volatility (SLV) models. The stochastic local volatility models studied in this paper include Heston model, 4/2 model, α-Hypergeometric model, stochastic alpha beta rho (SABR) model, Heston-SABR model and quadratic SLV model. Using the stochastic flow theorem, the closed-form CTMC approximation formula for the Greeks are obtained and the second order convergence rates are proved. Numerical examples confirm the theoretical findings.
KW - Continuous-time Markov chains
KW - Convergence rates
KW - Greeks
KW - Option pricing
KW - Stochastic local volatility models
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U2 - 10.1016/j.cam.2021.113901
DO - 10.1016/j.cam.2021.113901
M3 - Article
AN - SCOPUS:85118534465
SN - 0377-0427
VL - 404
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 113901
ER -