Black-Scholes

Why This Matters A derivative price can be computed two equivalent ways: as a risk-neutral expectation, or as the solution of a PDE. This is the Feynman-Kac result, which I explored in the earlier article. Monte Carlo is the natural way to handle the expectation, and the previous article 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. ...

Why This Matters Many of the world’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. ...