Statistical Methods in Finance 2016

Dec 18 - 22, 2016


A Kernel Estimator for Positive Time Series

by N Balakrishna

A jump-diffusion model for asset pricing is considered as an improvement over the geometric Brownian motion model in the classical Black-Scholes-Merton framework. The purpose of this lecture is to empirically fit the model to two benchmark Indian indices, namely, SENSEX and NIFTY. For this purpose, the various parameters for the jump-diffusion model are estimated empirically by using the adjusted daily closing prices for the years 2003-2012 for both the above mentioned indices. Three different mark processes, namely log-normal, log-uniform and log-double-exponential are considered. The maximum likelihood estimation technique is used to determine the best fit distribution from among these three. In case of SENSEX, the log-uniform and log-double-exponential models best fit the skewness and kurtosis respectively. In case of NIFTY, the log-double-exponential model gives the best fit to both.