Broker Strangle Algorithm for Volatility Surface

Broker Strangle Algorithm is used to calibrate FX volatility surface. At anchor expiry terms, the algorithm produces 25% and 10% Delta Call and Put volatilities from market at-the-money volatility, 25% and 10% Delta Risk Reversal and Broker Strangle volatility spreads.

The algorithm consists of solving a system of non-linear equations. When Left Delta quotation is used, nested non-linear equations are obtained as Left Delta leads by itself to solving a non-linear equation

Let us fix an anchor term and corresponding foreign and domestic interest rates (they will not appear in our notation, but they are crucial in this algorithm along with volatility data).

The Risk Reversal spreads (smile slope/distributional skewness) come then into picture via a volatility interpolation method. A 25% Delta Risk Reversal contract is a package made of a long 25% Delta Call position and a short 25% Delta Put position.

Repo Curve

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