Consider a stochastic differential equation (of the Ito type) dx=f(x)dt+g(x)dw where w is the standard Brownian motion (and thus dw/dt is the standard white noise.) Now consider a smooth function of x(t), say, u(x). What is the differential equation about u? Ito (whos is 93) says it should be du=u_{x}(f(x)dt+g(x)dw)+(1/2)u_{xx}[g(x)]^2dt
where the subscripts denote derivatives of first and second order. Note here that the first term is expected following the chain rule in (ordinary) calculus. However the second term is a surprise since it is a deterministic term reflecting a predictable behavior of the u(t) movement as a function of time. Now think x(t) as a stock price and u(t) as an option price you can see there is some gain in trading u rather than x since you would know better than folks who do not know Ito calculus. But of course this is all based on the white noise assumption and insider trading is always more deterministic :)