Is complicated math necessary for profitable trading?

An old blog post from Paul Wilmott addresses the too often accepted belief, "the more complicated the mathematics the better". An example he gave involves the Heston Stochastic Volatility Process, where you need to solve a PDE (Partial Differential Equation) involving numerical integration in complex space, i.e.

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So the next logical question remains, does all that work improve forecast accuracy significantly? More importantly, would it offer significantly more efficient volatility arbitrage strategies? We need empirical findings!


The fact that the above applies "standard arbitrage arguments", an assumption of no arbitrage, makes it not as desirable. Wilmott makes a really good point here, "So, many know all the ins and outs of the most advanced volatility models based in the classical no-arbitrage world. Well, what if your job is to find volatility arbitrage opportunities?"