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Fast-reversion Heston FX

This repo contains code for the fast-reversion Heston (FRH) model of Mechkov, 2015, which is a reparameterisation of the normal-inverse Gaussian (NIG) process, studied greatly by Barndorff-Nielsen, among others. In particular, one can produce implied volatility surfaces analytically (fourier transform), and verify them by simulation.

The key contribution here is an implementation of a simple dependence structure between multiple FRH models, as well as the measure change analytics required to consistently evaluate inverse and cross process. We provide a very simple simulation procedure, amenable to quasi-random sampling, and expose some very interesting volatility surface symmetries exhibited by this model.

Cross symmetry:

<img src="plots/surface-1.png" width="350"> <img src="plots/surface-2.png" width="350">

Sample paths:

<img src="plots/paths-1.png" width="350"> <img src="plots/paths-2.png" width="350">

Delta symmetry:

<img src="plots/surface-3.png" width="350"> <img src="plots/surface-4.png" width="350">

Market comparison:

<img src="plots/market-1.png" width="233"> <img src="plots/market-2.png" width="233"> <img src="plots/market-3.png" width="233"> <img src="plots/market-4.png" width="233"> <img src="plots/market-5.png" width="233"> <img src="plots/market-6.png" width="233">

Example jupyter notebooks are included which demonstrate usage. Tested with Python 3.5.2 and macOS Sierra 10.12.5.