TQBTHEQUANTBATEMAN
TQB/ learn/ fx/ butterflyEN · DARK
FXfront-officeinstrument

Butterfly

A convexity quote combining wing and ATM volatilities.

Reviewed 2026-08-10TheQuantBateman Research2 linked labs
01Intuition

Build the mental model first.

Butterfly asks how expensive both wings are relative to the centre.

ONE-LINE DEFINITION

A convexity quote combining wing and ATM volatilities.

02Mathematics

Now make it exact.

BFΔ=12(σcall,Δ+σput,Δ)σATMBF_{\Delta}=\tfrac12(\sigma_{call,\Delta}+\sigma_{put,\Delta})-\sigma_{ATM}
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Every model has a price.

01

Educational conventions are stated explicitly and may simplify market quotation or settlement details.

02

Rates are continuously compounded unless the section says otherwise.

03

Inputs are deterministic in the base model.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Why a quant cares.

Builds smile curvature alongside ATM and risk reversal quotes.

IntuitionMathematicsImplementationDesk risk
05Desk view
FRONT OFFICE VIEW

The hedge has opinions.

Start with the quote convention, then ask which FX risk survives the hedge. A number without its convention is merely well-dressed ambiguity.

Ask Bateman about this model
06Related

Continue through the graph.