A Methodological Approach to the Computational Problems in the Estimation of Adjusted Pin Model

Abstract

It is well documented that computational problems may lead to large biases in the estimation of probability of informed trading (PIN) models. The complexity of the AdjPIN model [Duarte, J. and Young, L., Why is PIN priced? J. Financ. Econ., 2009, 91, 119-138.], an extension of the conventional PIN model, exacerbates further these computational issues due to its larger parameter set. We introduce a dual approach to improve estimation reliability: a logarithmic factorization of the likelihood function and a strategic algorithm for generating initial parameter sets. The logarithmic factorization addresses floating point exceptions and numerical instability, while the algorithm significantly reduces the likelihood of converging to local maxima. We show that our methodology outperforms existing best practices and it enables accurate estimation of the AdjPIN model. We, therefore, strongly suggest its use in future studies.