Counterexamples for FX Options Interpolations -- Part I

TL;DR

This paper presents counterexamples where common FX option interpolation methods fail, highlighting potential risks in pricing and risk management of vanilla and exotic FX derivatives.

Contribution

It provides a list of specific counterexamples demonstrating the breakdown of popular FX option interpolation techniques.

Findings

Certain FX option interpolation methods can fail in specific scenarios

Counterexamples reveal limitations of existing interpolation models

Implications for risk management and model selection in FX derivatives

Abstract

This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but also more exotic derivatives which are typically valued with local volatility or local stochastic volatilility models.