Dupire on Inflection Quant Labhttps://inflection-quant.pages.dev/tags/dupire/Recent content in Dupire on Inflection Quant LabHugoen-usTue, 14 Jul 2026 00:00:00 +0000Forward and Backward Kolmogorov PDEs: An Intuitive Look at Their Dualityhttps://inflection-quant.pages.dev/articles/quant-foundations/forward_backward_pde/Tue, 14 Jul 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/forward_backward_pde/<h2 id="why-this-matters">Why This Matters</h2> <p>Most practitioners have seen the Black-Scholes PDE. It is a backward equation, closely related to the backward Kolmogorov PDE: fix a payoff at maturity, and the PDE propagates its value back to today.</p> <p>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 equation instead propagates a probability density forward from today, with the terminal value of the underlying and the maturity as its variables. This is the Fokker-Planck equation.</p>