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

Read the contractual cash flows first.

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

ONE-LINE DEFINITION

A convexity quote combining wing and ATM volatilities.

02Mathematics

Express payoff and present value precisely.

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

Make conventions part of the contract.

01

Contract dates, calendars, settlement, notionals and payoff currency are part of the valuation input.

02

Discounting and projection conventions must match the collateral and quotation framework.

03

The displayed payoff omits legal terms and lifecycle events unless stated otherwise.

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

Locate the quote and replication instruments.

Builds smile curvature alongside ATM and risk reversal quotes.

Intuition→Mathematics→Implementation→Desk risk
05Desk view
FRONT OFFICE VIEW

Map cash-flow changes into hedge risk.

Reconcile the contractual payoff before reading the FX risk. Small date or convention changes can move cash flows before any model parameter moves.

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06Related

Continue to the nearest instrument or model.