This paper simulates the path of Indian Index (Nifty) spot prices based on two different classes of parametric distributions, namely, Gaussian distribution (geometric Brownian motion) and non-Gaussian distributions, viz., normal inverse Gaussian (NIG), and Tsallis distributions. The classical option-pricing theories, such as the Black-Scholes model, posit Gaussian distribution in the asset-returns. The stylised facts reveal that asset-returns are not Gaussian and have fat-tails and skewness (non-Gaussian) characteristics. Going forward, several research papers investigated the option-pricing dynamics assuming non-Gaussian distribution in the return-distribution such as Normal Inverse Gaussian. Borland (2002) formulated a closed-form option pricing model assuming another class of non-Gaussian distribution, i.e., Tsallis (q-Gaussian) distribution in the asset returns.
This study seeks to understand which class of distribution (Gaussian or non-Gaussian) fits the Nifty spot prices better. Simulations are run for a six-year window (2006 to 2011). These six years are divided into 24 sub-periods. For each sub-period of three months, Nifty spot prices are simulated. The start date of a sub-period is fixed on the start date of a 3-month Nifty option, and the initial price of all three simulations is calibrated to the closing price of Nifty on that day. Five thousand paths of Nifty spot prices are generated from each of the simulations. The Nifty spot price at the end of the option-expiry date is compared with the mean, median, and percentile-interval Nifty prices predicted by each of the simulations. Results show that Tsallis distribution best predicts the Nifty return-distribution among these three classes of distributions in terms of consistency and efficiency. The consistency of the results is examined by three pre-defined sample periods (pre-crisis, crisis, and post-crisis). Results reveal that Tsallis distribution is robust, consistent, and efficient and can explicate Nifty return-distribution in all the market conditions.
