Adaptive SOR Method for Implied Volatility Calculation

In a recent blog contribution Fabien Le Floc’h [1] suggests to combine the adaptive successive over-relexation method [2] with an improved explicit approximate implied volatility formula [3] to calculate the initial guess. The implementation of both algorithms is straight forward.

A large set of OTM and ITM options together with different displacement factors has been identified to serve as a benchmark portfolio to compare the performance with the original QuantLib implementation. As can be seen in the diagram below the new method is – depending on the accuracy – two to three times faster than the current QuantLib implementation.

sorThe implementation is available here, the diagram above is derived from the test case testImpliedVolAdaptiveSuccessiveOverRelaxation in the class BlackFormulaTest.

[1] Le Floc_h, F (2017) Implied Volatility from Black Scholes Price

[2] Li, M. (2008) An Adaptive Successive Over-relaxation Method for Computing the Black-Scholes Implied Volatility

[3] J. Gatheral, I. Matic, R. Radoicic, D. Stefanica (2017), Tighter Bounds for Implied Volatility