Adaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inference

Qian, Yiyuan1; Zhang, Kai1; Li, Jingzhi2; Wang, Xiaoshen3

2022

10.3934/era.2022119

ELECTRONIC RESEARCH ARCHIVE   Impact Factor & Quartile

2688-1594

In this paper, we propose an adaptive neural network surrogate method to solve the implied volatility of American put options, respectively. For the forward problem, we give the linear complementarity problem of the American put option, which can be transformed into several standard American put option problems by variable substitution and discretization in the temporal direction. Thus, the price of the option can be solved by primal-dual active-set method using numerical transformation and finite element discretization in spatial direction. For the inverse problem, we give the framework of the general Bayesian inverse problem, and adopt the direct Metropolis-Hastings sampling method and adaptive neural network surrogate method, respectively. We perform some simulations of volatility in the forward model with one- and four-dimension to compare the point estimates and posterior density distributions of two sampling methods. The superiority of adaptive surrogate method in solving the implied volatility of time-dependent American options are verified.

adaptive neural network surrogate method primal-dual active-set method far-field technique Bayesian inverse problem Metropolis-Hastings sampling

SCI

English

Others

NSF of China[11871245,11971221,11731006] ; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University[93K172018Z01] ; Shenzhen Sci-Tech Fund["JCYJ20190809150413261","JCYJ20170818153840322"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Mathematics

Mathematics

WOS:000807184900001

AMER INST MATHEMATICAL SCIENCES-AIMS

Web of Science

1.Jilin Univ, Dept Math, Changchun 130012, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA

Qian, Yiyuan,Zhang, Kai,Li, Jingzhi,et al. Adaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inference[J]. ELECTRONIC RESEARCH ARCHIVE,2022,30(6).

Qian, Yiyuan,Zhang, Kai,Li, Jingzhi,&Wang, Xiaoshen.(2022).Adaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inference.ELECTRONIC RESEARCH ARCHIVE,30(6).

Qian, Yiyuan,et al."Adaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inference".ELECTRONIC RESEARCH ARCHIVE 30.6(2022).