https://inflection-quant.pages.dev/tags/black-scholes/Recent content in Black-Scholes 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>https://inflection-quant.pages.dev/articles/quant-foundations/quanto_and_compo/Tue, 19 May 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/quanto_and_compo/<h2 id="why-this-matters">Why This Matters</h2> <p>Many of the world&rsquo;s most actively traded commodities are priced in USD, yet end investors and corporates often operate in other currencies. A Canadian oil producer hedging output, a European airline managing jet fuel costs, or an Asian sovereign wealth fund allocating to commodity exposure all face the same underlying issue: commodity risk does not exist in isolation from FX risk. The standard approach is to hedge the commodity leg with USD-denominated futures or swaps and manage FX separately through forwards or options. This works, but it treats the two risks as independent. Quanto and compo options take a different approach by packaging both risks into a single instrument, but the way each handles FX risk creates some pricing and hedging subtleties that I find are easy to miss.</p>