A DETAILED EXAMINATION OF LOCAL COMPOSITE QUANTILE REGRESSION IN STOCHASTIC DIFFUSION MODELS

In this paper, we delve into the realm of Composite Quantile Regression (CQR) for parameter estimation within the context of diffusion models. While CQR has found utility in classical linear regression models and general non-parametric regression models, it has yet to be explored extensively in the domain of diffusion models. The diffusion model we consider operates within the framework of a filtered probability space (Ω, F, (Ft)t≥0, P), described by the stochastic differential equation:dXt = β(t)b(Xt)dt + σ(Xt)dWt,where β(t) is a time-dependent drift function, σ(⋅) and b(⋅) are known functions. Notably, this model encompasses several renowned option pricing models 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.Our exploration of CQR in diffusion models seeks to provide a robust framework for estimating regression coefficients in scenarios with intricate dynamics. By extending CQR to this domain, we aim to enhance our understanding of parameter estimation in diffusion models and contribute valuable insights to financial modeling and related fields.