FX Volatility Smile
Construct an FX smile from ATM, risk reversal and butterfly quotes.
Name the object before manipulating it.
FX desks quote the centre, asymmetry and wing richness rather than every strike directly.
Construct an FX smile from ATM, risk reversal and butterfly quotes.
State the governing relationship.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Draw the boundary of the claim.
Definitions, units and information sets are fixed before the mathematical relationship is applied.
Rates and volatilities use decimal units and time uses year fractions unless stated otherwise.
The relationship is local to its stated assumptions and should not be extrapolated mechanically.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Connect the definition to an observable.
Vanilla marking, strike construction and exotic calibration.
Translate the concept into a risk question.
State the convention, identify the observable and ask which FX risk remains after the proposed hedge.
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