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Bayesian synthetic likelihood for stochastic models with applications in mathematical finance
[摘要] We present a Bayesian synthetic likelihood method to estimate both the parameters and their uncertainty in systems of stochastic differential equations. Together with novel summary statistics the method provides a generic and model-agnostic estimation procedure and is shown to perform well even for small observational data sets and biased observations of latent processes. Moreover, a strategy for assessing the goodness of the model fit to the observational data is provided. The combination of the aforementioned features differentiates our approach from other well-established estimation methods. We would like to stress the fact that the algorithm is pleasingly parallel and thus well suited for implementation on modern computing hardware. We test and compare the method to maximum likelihood, filtering and transition density estimation methods on a number of practically relevant examples from mathematical finance. Additionally, we analyze how to treat the lack-of-fit in situations where the model is biased due to the necessity of using proxies in place of unobserved volatility.
[发布日期] 2023-06-05 [发布机构] 
[效力级别]  [学科分类] 
[关键词] synthetic likelihood;SDE systems;parameter estimation;MCMC sampling;goodness of fit;financial models;stochastic volatility [时效性] 
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