Vanna-Volga methods applied to FX derivatives : from theory to market practice

TL;DR

This paper explores Vanna-Volga methods for pricing FX exotic options, providing theoretical justification, market data treatment, and a calibration approach to align model outputs with observed market prices.

Contribution

It offers a theoretical foundation for Vanna-Volga methods, adapts them for exotic options, and introduces a calibration technique using one-touch prices.

Findings

Vanna-Volga methods closely match market prices for FX options

Calibration improves the accuracy of Vanna-Volga pricing

The approach is validated against sophisticated models

Abstract

We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival' and the `expected first exit time'. Since the methods rely heavily on the appropriate treatment of market data we also provide a summary of the relevant conventions. We offer a justification of the core technique for the case of vanilla options and show how to adapt it to the pricing of exotic options. Our results are compared to a large collection of indicative market prices and to more sophisticated models. Finally we propose a simple calibration method based on one-touch prices that allows the Vanna-Volga results to be in line with our pool of market data.