A neural network learns the residual error to Hagan's SABR implied volatility approximation using geometry-aware inputs derived from the model's SDEs.
arXiv preprint , year =
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abstract
We present a neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models -including the rough volatility family- and a range of derivative contracts. The aim of neural networks in this work is an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. We highlight how this perspective opens new horizons for quantitative modelling: The calibration bottleneck posed by a slow pricing of derivative contracts is lifted. This brings several numerical pricers and model families (such as rough volatility models) within the scope of applicability in industry practice. The form in which information from available data is extracted and stored influences network performance: This approach is inspired by representing the implied volatility and option prices as a collection of pixels. In a number of applications we demonstrate the prowess of this modelling approach regarding accuracy, speed, robustness and generality and also its potentials towards model recognition.
fields
q-fin.CP 2years
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A Geometry-Aware Residual Correction of Hagan's SABR Implied Volatility Formula
A neural network learns the residual error to Hagan's SABR implied volatility approximation using geometry-aware inputs derived from the model's SDEs.
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