https://inflection-quant.pages.dev/tags/heat-equation/Recent content in Heat-Equation on Inflection Quant LabHugoen-usTue, 09 Jun 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/fdm/Tue, 09 Jun 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/fdm/<h2 id="why-this-matters">Why This Matters</h2> <p>A derivative price can be computed two equivalent ways: as a risk-neutral expectation, or as the solution of a PDE. This is the <a href="../../articles/quant-foundations/feynman_kac/">Feynman-Kac result</a>, which I explored in the earlier article. Monte Carlo is the natural way to handle the expectation, and the <a href="../../articles/quant-foundations/mc_variance_reduction/">previous article</a> worked through techniques for making it more efficient. Here I want to look at the other side, where the price is the solution of a PDE and we solve it on a grid.</p>