Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels

Abstract

This paper proposes an asymmetric kernel-based method for nonparametric estimation of scalar diffusion models of spot interest rates. We derive the asymptotic theory for the asymmetric kernel estimators of the drift and diffusion functions for general and positive recurrent processes and illustrate the advantages of the Gamma kernel for bias correction and efficiency gains. The finitesample properties and the practical relevance of the proposed nonparametric estimators for bond and option pricing are evaluated using actual and simulated data for U.S. interest rates.

Nonparametric Estimation for Second-Order Jump-Diffusion Model in High Frequency Data

“…• From Table 4 -6, the absolute mean of bias and variance for estimator constructed with Gamma asymmetric kernels are less than that constructed with Gaussian symmetric kernels, which indicates that compared with that constructed with Gaussian symmetric kernels, estimator constructed with Gamma asymmetric kernels is practically unbiased and exhibits smaller variability for either the boundary point or the spare design point. This coincides with the discussion of coverage rate in Remark 10, as documented in Gospodinov and Hirukawa [18].…”

“…In practice, we can take the plug-in method studied in Fan and Gijbels [13] to obtain an optimal smoothing bandwidth h n on behalf of MSE. As mentioned in Gospodinov and Hirukawa [18], the bandwidth h n constructed above relies on the consistent estimators for these unknown quantities and they are difficult to obtain and may give rise to bias. Moreover, Hagmann and Scaillet [23], regarding global properties, discussed the choice of bandwidth to ameliorate the adaptability of Gamma asymmetric kernel estimators since the bandwidth h n constructed above varies with the change of the design point x.…”

“…In conclusion, asymmetric kernels is a combination of a boundary correction device and a "variable bandwidth" method. For a review of application using asymmetric kernels, one should refer to Chen [7] [8] to estimate densities, Chen [9] to estimate a regression curve with bounded support, Bouezmarni and Scaillet [4] to apply the asymmetric kernel density estimators to income data, Kristensen [29] to consider the realized integrated volatility estimation, Gospodinov and Hirukawa [18] to propose an asymmetric kernel-based method for scalar diffusion models of spot interest rates, compared with Stanton [46], to show that asymmetric kernel smoothing is expected to reduce substantially both the bias near the origin and the bias that occurs for high values in the estimation of the drift coefficient. Hanif [21] addressed local linear estimation using Gamma asymmetric kernels for the infinitesimal moments in model (1).…”

Uniform Convergence Rates of Kernel-Based Nonparametric Estimators for Continuous Time Diffusion Processes: A Damping Function Approach

“…This slower convergence occurs because we cannot use the symmetricity property of the kernel in the neighborhood of zero (i.e., R xK (x) dx = 0) to kill the …rst-order term of the smoothing bias (therefore, if I 6 = R, the use of higher-order kernels does not improve the uniform convergence rate over I). This kind of phenomenon, the so-called boundary bias, is observed if the endpoint of the support is bounded and the symmetric kernel is used (see the arguments in Bouezmarni and Scaillet, 2005), while the boundary bias may be avoided by using asymmetric kernels as in Bouezmarni et al (2005) and Gospodinov and Hirukawa (2012). We note that the supremum is taken over the open set (0; 1) in (S.38), which is for avoiding the inde…niteness at x = 0 when I = [0; 1) and (0) is unbounded (we may have [0; 1) in (S.38) if 0 is a point attainable by the process and (0) < 1).…”

Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

“…Chen 2000;Jin and Kawczak 2003;Scaillet 2004) have emerged as a viable alternative that can accommodate the stylised facts. Although the kernels are relatively new in the literature, several papers report favourable evidence from applying them to empirical models in economics and finance; see, for instance, Section 1 of Gospodinov and Hirukawa (2012) for a non-exhaustive list of the papers. The reason why asymmetric kernels tend to work well for the distributions with two stylised facts is their property as a combination of a boundary correction device and adaptive smoothing that has effect similar to the variable bandwidth methods.…”