Not a lot of it is statistical arbitrage - yes this is what Rennaisance and D.E. Shaw do, but this is not what banks (sans perhaps Goldman Sachs) devote much of their compute power to. It's just too hard to make money doing this compared to more traditional activities like market making.
As stated, risk management is a big application: VaR and market stress scenarios are computationally intensive, particularly for portfolios with path-dependent derivatives. Pricing is the other big application: it is similarly computationally intensive to value derivatives against the market-implied term structure of volatility.
That is: you look at the historical prices of all commodities over time and try to figure out which ones tend to vary together (eg copper-mining companies go up when copper prices go up... but you're looking for less obvious examples than that). Then you look at whether current prices diverge from these trends at all, and if they do you buy/sell accordingly. At least, that's the handwavey version I know -- I'm sure whatever they're doing at Rennaisance and DE Shaw is something I don't even know about.