Discussing the article: "From Delta-Space Quotes to the FX Volatility Smile: Garman-Kohlhagen and the Convention Problem"

 

Check out the new article: From Delta-Space Quotes to the FX Volatility Smile: Garman-Kohlhagen and the Convention Problem.

FX options are quoted in delta space, not by strike. This article implements an FX-native smile tool for MetaTrader 5: it converts ATM, risk reversal and butterfly quotes into strike-space pillars, prices with the Garman–Kohlhagen model, handles spot/forward and premium-adjusted delta conventions per pair, and draws the smile with a reconstructed strike ladder and Greeks.

MetaTrader 5 is, at its core, a foreign-exchange platform. Yet the options tooling that has grown up around it is built in the equity idiom. In earlier articles we built an implied-volatility surface and a dealer gamma-exposure map, both of which start from a listed chain of strikes and price it with plain Black-Scholes. That is the right model for an index option. For a currency it is the wrong parameterisation, since the single-rate version has no slot for the yield the base currency earns, and it says nothing about how the FX market actually quotes. This article fills that gap with a standalone build, the FX-native counterpart to the surface tool, running the pipeline in the FX direction: from the delta-space quotes a desk publishes to the strike-space smile they imply.

Two things make FX options their own world, and both drive the code here. First, the pricing model is Garman-Kohlhagen, Black-Scholes with two interest rates instead of one, because a currency pays a continuous yield equal to its own money-market rate. Second, and more subtly, the delta itself is a market convention: it can be measured on the spot or the forward, and premium-adjusted or not. Most retail material glosses over this. We do not, implementing all four conventions, tabulating which pair uses which, and measuring how far the choice actually moves a strike.

By the end you will have a working tool: a pricing-and-convention header, a reconstruction engine, two interchangeable data providers, and a chart indicator that draws the delta-space smile with the reconstructed strike ladder printed on the curve. We assume you know what an option and an implied volatility are; we do not re-derive Black-Scholes, we adapt it.

The FX volatility smile in delta space: ATM, risk reversal as tilt, butterfly as wing-lift

Author: Muhammad Minhas Qamar