Comparative Analysis of Asset Pricing Models Based on Log-Normal Distribution and Tsallis Distribution using Recurrence Plot in an Emerging Market

TLDR: This simulation simulates two distinct time series based on initial data from NIFTY daily close values, one based on the Gaussian return distribution and the other on non-Gaussian distribution, which gives a definite edge to the non- Gaussian model over theGaussian one.

Abstract: It has long been challenged that the distributions of empirical returns do not follow the log-normal distribution upon which many celebrated results of finance are based including the Black–Scholes Option-Pricing model. Borland (2002) succeeds in obtaining alternate closed form solutions for European options based on Tsallis distribution, which allow for statistical feedback as a model of the underlying stock returns. Motivated by this, we simulate two distinct time series based on initial data from NIFTY daily close values, one based on the Gaussian return distribution and the other on non-Gaussian distribution. Using techniques of non-linear dynamics, we examine the underlying dynamic characteristics of both the simulated time series and compare them with the characteristics of actual data. Our findings give a definite edge to the non-Gaussian model over the Gaussian one.