Modeling of Measurement Error in Financial Returns Data

ArXiv ID: 2408.07405 “View on arXiv”

Authors: Unknown

Abstract

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [“12”] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data.

Keywords: Lévy Process, Measurement Error, Multilevel MCMC, Bayesian Inference, Fund Returns, Fund Returns

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including Lévy processes, stick-breaking representations, and multilevel Monte Carlo theory. It demonstrates empirical rigor through a developed MCMC algorithm, implementation on real fund data, and analysis of computational cost reduction.

  flowchart TD
    A["Research Goal<br>Model measurement error<br>in discretely observed<br>financial returns and maxima"] --> B["Methodology<br>Develop stochastic model<br>using Lévy process &<br>stick-breaking approximation"]
    B --> C["Data Inputs<br>Time-series of log-returns<br>and associated maxima"]
    B --> D["Computational Process<br>Bayesian inference via<br>Multilevel MCMC<br>for posterior sampling"]
    C --> D
    D --> E["Key Findings<br>Approximated posterior distributions<br>for fund returns<br>and improved computational efficiency"]