Normality?

There is a lot (roughly 328 Million search results in google) said and talked about normality, specifically in the returns distributions of the traded assets. I am not well equipped to comment about the recurrent use of normality (say in the Black-Scholes) but my guess is that it is perhaps the simplest heuristic to adopt given other more complex distributions (say an EVD).

But we can always work our way moving up from the simpler assumptions, keeping the assumptions in mind when it comes to action. For example option traders and market-makers know too well that volatility (Implieds) does not flow in a straight line across time and price dimensions but rather takes a curvy shape which is nicely called as skews. So knowing the empirical returns distributions is quite useful in building skews etc. I took the S&P Emini H15 futures contract for 5 minute, 15 minute and the 1 hour bars and compared their return distributions against the theoretical normal ones. The graphs plotted below with the CDFs and the Q-Q plots as well. I also ran a Shapiro test on the returns just to confirm the non-normality. Knowing the changing shapes of empirical versus the theoretical definitely helps in anticipating price moves/bias.

The normality test result is below:

shapiro.test(cc) Shapiro-Wilk normality test data: cc W = 0.8325, p-value < 2.2e-16

Originally published at https://www.linkedin.com.