Open AccessAdaptive neural network surrogate model for solving the implied volatility of time-dependent American option via Bayesian inference
Author(s) -
Yiyuan Qian,
Kai Zhang,
Jingzhi Li,
Xiaoshen Wang
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022119
Subject(s) - artificial neural network , discretization , computer science , bayesian inference , mathematical optimization , volatility (finance) , inverse problem , bayesian probability , surrogate model , mathematics , econometrics , algorithm , artificial intelligence , mathematical analysis
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.