Forward and Backward Kolmogorov PDEs: An Intuitive Look at Their Duality
Why This Matters Most practitioners have seen the Black-Scholes PDE. It is closely related to the backward Kolmogorov PDE: fix a payoff at maturity, and the equation propagates its value back to today. There is also a forward equation, which may be less familiar. The backward equation has current spot and current time as its variables and takes the payoff as a terminal condition. The forward one instead propagates a probability density forward from today, with the terminal value of the underlying and the maturity as its variables. This is Fokker-Planck. ...