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.

Kousik Guhathakurta

Finance and Accounting

Basabi Bhattacharya

A Roy Chowdhury

<p>IIM Indore seeks to be a contextually-relevant business school with world-class academic standards that develops socially-conscious managers, leaders and entrepreneurs. IIM Indore is committed to: Excellence in management education, research, and training, Use of contemporary participant-centric pedagogies and teaching methods, A presence in emerging segments of management education.</p>

IIM Indore

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

Research in Finance The Spread of Financial Sophistication through Emerging Markets Worldwide

Behaviour of non-linearity in stock markets of developed countries has been empirically evidenced for quite some time. Some few studies examine non-linearity of emerging stock markets as well. A comprehensive overview of stock market behaviour in terms of non-linearity is undertaken in this study where several non-linearity test approaches have been applied on both the developed and emerging country groups. For the purpose we have selected seven stock exchanges from developed markets (UK, Germany, Australia, New Zealand, Hong Kong, France and Japan) and seven from emerging markets (Hungary, Chile, Mexico, Malaysia, Taiwan, China and India). Taking their daily close data covering a period from January 2005 to July 2011, we have investigated the presence of nonlinearity in the data sets and tried to find out whether there is any difference amongst them in this regard. We have first used the test method developed by Brock, Dechert and Scheinkman (BDS) and examine the non-linearity feature in each of the time series. To reinforce our findings, we have conducted the White's Neural Network tests on the same data set. Additionally, we have also performed the Keenan's test for non-linearity. Another popular non-linear test is the Hinich bi-spectrum test, which involves estimating the bi-spectrum of the observed time series. We have further used this test to find out whether it detects non-linearity in these time series. Another linearity test for time series was introduced based on concepts from the theory of neural networks. Ter"asvirta et al. developed its power fully. We have applied this Ter"asvirta Neural Network test as a final reinforcement of our findings.

International Trade and International Finance

Testing Non-linearity in Emerging and Developed Markets

<p>Recurrence Plots are graphical tools based on Phase Space Reconstruction. Recurrence Quantification Analysis (RQA) is a statistical quantification of RPs. RP and RQA are good at working with non-stationarity and noisy data, in detecting changes in data behavior, in particular in detecting breaks, like a phase transition and in informing about other dynamic properties of a time series. Endogenous Stock Market Crashes have been modeled as phase changes in recent times. Motivated by this, we have used RP and RQA techniques for detecting critical regimes preceding an endogenous crash seen as a phase transition and hence give an estimation of the initial bubble time. We have used a new method for computing RQA measures with confidence intervals. We have also used the techniques on a known exogenous crash to see if the RP reveals a different story or not. The analysis is made on Nifty, Hong Kong AOI and Dow Jones Industrial Average, taken over a time span of about 3 years for the endogenous crashes. Then the RPs of all time series have been observed, compared and discussed. All the time series have been first transformed into the classical momentum divided by the maximum Xmax of the time series over the time window which is considered in the specific analysis. RPs have been plotted for each time series, and RQA variables have been computed on different epochs. Our studies reveal that, in the case of an endogenous crash, we have been able to identify the bubble, while in the case of exogenous crashes the plots do not show any such pattern, thus helping us in identifying such crashes. extcopyright 2010 Elsevier B.V. All rights reserved.</p>

Physica A: Statistical Mechanics and its Applications

Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes

The World Scientific Handbook of Futures Markets World Scientific Handbook in Financial Economics Series

Proof that Properly Anticipated Prices Fluctuate Randomly

Physics Letters A

Confidence bounds of recurrence-based complexity measures

IEEE Transactions on Information Theory

Generalized Box–MÜller Method for Generating $q$-Gaussian Random Deviates

Journal	Research in Finance The Spread of Financial Sophistication through Emerging Markets Worldwide
Publisher	Emerald Group Publishing Limited
ISSN	0196-3821
Open Access	No