In the classical Black and Scholes framework, stock options are priced under the assumption that stock prices are modeled according to lognormal processes, driven by instantaneously correlated Brownian motions. It follows that Hang Seng Index (HSI), a linear combination of stock prices of its constituents, does not undergo lognormal process. We aim to investigate if there is arbitrage if we simply assume HSI to follow a lognormal process. By considering a hedging strategy, we used historical data of option prices of HSI and its constituents to test if there is any arbitrage. We consider the distributional difference in these two models. We give explanation to the problem by using Kullback-Leibler information (KLI), Hellinger distance (HD) and Exponential Manifold of densities. Finally,...[ Read more ]

In the classical Black and Scholes framework, stock options are priced under the assumption that stock prices are modeled according to lognormal processes, driven by instantaneously correlated Brownian motions. It follows that Hang Seng Index (HSI), a linear combination of stock prices of its constituents, does not undergo lognormal process. We aim to investigate if there is arbitrage if we simply assume HSI to follow a lognormal process. By considering a hedging strategy, we used historical data of option prices of HSI and its constituents to test if there is any arbitrage. We consider the distributional difference in these two models. We give explanation to the problem by using Kullback-Leibler information (KLI), Hellinger distance (HD) and Exponential Manifold of densities. Finally, we analyse how the above distances change according to the parameter values.