On Calibration of Mathematical Finance Models by Hypernetworks

Abstract

The process of fitting mathematical finance (MF) models for option pricing - known as calibration - is expensive because evaluating the pricing function usually requires Monte-Carlo sampling. Inspired by the success of deep learning for simulation, we present a hypernetwork based approach to improve the efficiency of calibration by several orders of magnitude. We first introduce a proxy neural network to mimic the behaviour of a given mathematical finance model. The parameters of this proxy network are produced by a hyper-network conditioned on the parameters of the corresponding MF model. Training the hyper network with pseudo-data fits a family of proxy networks that can mimic any MF model given its parameters, and produce accurate prices. This amortises the cost of MF model fitting, which can now be performed rapidly for any asset by optimising w.r.t. the input of the hypernetwork. Our method is evaluated with S &P 500 index option data covering three million contracts over 15 years, and the empirical results show it performs very closely to the gold standard of calibrating the mathematical finance models directly, while boosting the speed of calibration by 500 times. The code is released at https://github.com/qmfin/HyperCalibration .