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This study is intended to investigate the volatility patterns in Bombay Stock Exchange Limited Sensitivity Index (BSE Sensex) based on time series data collected for 10 years period of time. To reach out the predefined objectives of the study, the authors have employed generalized autoregressive conditional heteroscedastic models. The study revealed that the presence of heteroscedasticiy is found in BSE Sensex. Further, the model produced highly accurate results when the researchers compared the estimated results from actual. Furthermore, the volatility of BSE Sensex has shown the features of clustering and significant time varying. Moreover, the model has indicated that there is a positive correlation between daily stock returns and the BSE Sensex volatility.

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.

The ups and downs of the stock markets are consistently in the news. All things considered, there's no end to reporting the trajectory of volatility. Wide value changes in stock prices are a daily event in any stock market as speculators respond to monetary, business, and political situations. The main question is − did the Indian stock market develop a speculative bubble during the time of the US subprime crisis? Also, in terms of knowledge gained for an investor or a policy maker, we ask the following question: As to what extent are speculative bubbles predictable during a financial crisis? Knowledge gained by investors is also a part and parcel of an applied knowledge economy in a broader dimension.

In this chapter, the authors use a speculative bubble tracker, based on a Wiener stochastic process, to check for the existence of speculative bubbles during the 2008–2009 US subprime crisis. The data used in the study are daily SENSEX values (i.e., combination of stock prices of 30 well-established, most actively traded stocks of financially sound companies listed in the Bombay Stock Exchange) for the period between December 2007 and December 2009. Using such forms of daily data, the authors trace out the price movements using a Brownian motion equation and hence, try to correlate the stock price fluctuations with fluctuations in the crisis index (as put together by the authors) in the Indian context. Interestingly, for India, such a speculative bubble was prevalent during the time period considered pertaining to the 2008 US subprime crisis.

Summing up, the implication in terms of knowledge gained is particularly of interest for the portfolio managers who are engaged in devising diversification strategies for their portfolios.