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BAYESIAN MODELING OF FINANCIAL DATA USING ESSCHER TRANSFORMED LAPLACE DISTRIBUTION IN STAN
Keywords:
Bayesian inference, leave-one-out cross-validation, Stan, Watanabe-Akaike information criterionDOI:
https://doi.org/10.17654/0972361725046Abstract
This study investigates the application of Bayesian methods for estimating parameter of the Esscher transformed Laplace distribution, renowned for its ability to capture the asymmetry and heavy tails commonly observed in financial data. This paper also focuses on the Bayesian estimation of stress strength parameter using both squared error and LINEX loss functions. A simulation study is conducted to compare the performance of the proposed Bayesian estimators for the unknown parameter and stress strength parameter with maximum likelihood estimator based on mean squared error. For the simulation study, we employ Gibbs sampling within the Metropolis-Hastings framework using Markov Chain Monte Carlo techniques to obtain Bayesian estimates. Utilizing R software and the Stan programming language, we analyze real-world stock price data and demonstrate how Bayesian estimators leverage advanced Markov Chain Monte Carlo techniques, particularly the No-U-Turn Sampler. The fit of the model is assessed using a Bayesian approach, utilizing information criteria such as Deviance Information Criterion, Watanabe-Akaike Information Criterion and leave-one-out cross-validation.
Received: January 24, 2025
Accepted: April 9, 2025
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