Local Volatility: From the Implied Vol Surface to Risk-Neutral Dynamics

Why This Matters In an earlier article we constructed the implied volatility surface and used it primarily to price vanilla options. But a great deal of what trades is not vanilla. Products like barriers and autocallables depend on the path the underlying takes, not only where it lands. Suppose I price a barrier by Monte Carlo. At each step the spot sits at some level, and I need a volatility to advance it. What vol do I use? The surface gives me a vol for every strike, but simulation does not ask about strikes. It asks what volatility the spot experiences at this level, at this moment, which the surface cannot answer. ...

July 23, 2026

Constructing the Implied Volatility Surface: From Market Quotes to an Arbitrage-Free Fit

Why This Matters For vanilla options, the simple models are usually sufficient. A plain call or put can be priced off Black-Scholes directly; you often do not need to reach for local volatility or a stochastic volatility model. Those heavier models earn their place with exotics, where the payoff depends on how the smile behaves rather than just its level today. For a vanilla, you take the market’s implied volatility at the relevant strike and maturity and feed it into Black-Scholes. But that assumes a volatility surface already exists: before Black-Scholes can price anything, the surface it reads from has to be built, and building it is less straightforward than it appears. ...

June 26, 2026

Quanto vs Compo Commodity Options: The Role of FX in Pricing and Risk

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. ...

May 19, 2026

Futures-Style Margined Options: The Absence of Early Exercise Premium

Why This Matters When I first studied options, most textbook examples were equity-style: you pay a premium upfront, and you receive the payoff at expiry, or when you choose to exercise for American options. That framing was so ingrained that I assumed it was the general case. When I started working on commodity derivatives, I encountered a different world. Many options are traded under futures-style margining. No premium changes hands at inception; instead, the option is margined daily like a futures contract. The convention tends to split along venue lines rather than by underlying. US exchanges are predominantly equity-style: options on WTI crude futures at the CME and options on corn and wheat futures at the CBOT all require an upfront premium. European venues lean the other way. Options on ICE Brent futures and options on EUA carbon futures at ICE Endex and EEX are both margined futures-style. ...

April 23, 2026