Variance-Reduction on Inflection Quant Labhttps://inflection-quant.pages.dev/tags/variance-reduction/Recent content in Variance-Reduction on Inflection Quant LabHugoen-usTue, 02 Jun 2026 00:00:00 +0000Monte Carlo Variance Reduction: What We Average, and How We Samplehttps://inflection-quant.pages.dev/articles/quant-foundations/mc_variance_reduction/Tue, 02 Jun 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/mc_variance_reduction/<h2 id="why-this-matters">Why This Matters</h2> <p>In the article on the <a href="../../articles/quant-foundations/feynman_kac/">Feynman-Kac theorem</a>, we saw that the price of a derivative can be expressed equivalently as the solution to a deterministic PDE or as the expectation of a discounted payoff under the risk-neutral measure. This gives us two complementary numerical approaches to pricing. For low-dimensional problems with smooth payoffs, finite difference methods on the PDE side are efficient and accurate. For high-dimensional problems, path-dependent payoffs, or models where the PDE is hard to derive, Monte Carlo (MC) on the expectation side becomes the natural choice.</p>