UNVEILING THE CONSTRAINING ATTRIBUTES OF LOCAL AGGREGATE QUANTILE REGRESSION IN DISSEMINATION MODELS

Abstract

This paper introduces a novel approach for parameter estimation within the context of diffusion models. While composite quantile regression (CQR) has been applied effectively in classical linear regression models and more recently in general non-parametric regression models, its application in diffusion models has been limited. This research bridges this gap by extending CQR to estimate regression coefficients in diffusion models. The diffusion model is considered within the framework of a filtered probability space (Ω, F, (Ft)t≥0, P), represented as: dXt = β(t)b(Xt)dt + σ(Xt)dWt, where β(t) represents a time-dependent drift function, Wt is the standard Brownian motion, and b(⃗) and σ(⃗) are known functions. Notably, Model (1.1) encompasses several well-known option pricing and interest rate term structure models, including Black and Scholes (1973), Vasicek (1977), Ho and Lee (1986), and Black, Derman, and Toy (1990), among others. This study extends the applicability of CQR to diffusion models, offering a powerful tool for estimating regression coefficients in this context. It fills a significant research gap, providing a promising avenue for enhanced parameter estimation in the field of diffusion models.