We investigate the consistency of classes of local-stochastic volatility (LSV) models with respect to spot inversion and multiplication, and hence their applicability in the foreign exchange market. We consider two main classes, one based on the Heston model and one based on the SABR model. Then we embed them in a more general superclass of LSV models. We give general conditions the models in the superclass must satisfy to be invariant with respect to inversion and check these conditions for a collection of popular LSV models. We also investigate affine diffusion processes, showing that the symmetry conditions for inversion are automatically fulfilled. We draw conclusions on the arbitrage opportunity in variance swaps. With respect to multiplication, we consider a Heston-based class only and show that, in order for consistency to be preserved, an adjustment in the drift of the exchange rate dynamics is required. 

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/32462 must be provided.

1. Stability of calibration procedures: fractals in the Black-Scholes model
2. Improvement of numerical option pricing methods based on the Hilbert transform using spectral filtering