Pricing FX Options under Intermediate Currency

TL;DR

This paper introduces an intermediate currency method for consistent FX option pricing across multiple markets using a unified risk-neutral measure, simplifying calibration and ensuring price consistency.

Contribution

It proposes a novel intermediate currency framework that enables simultaneous FX option pricing across markets, applicable to various stochastic volatility models and model-free approaches.

Findings

The approach ensures consistent option prices across all FX markets.

Calibration to domestic volatility smile suffices for multi-market pricing.

The method is demonstrated with Heston, SABR, and distribution-based models.

Abstract

We suggest an intermediate currency approach that allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is sufficient to calibrate a model to the volatility smile on the domestic market as, due to the consistency of pricing formulas, the model automatically reproduces the correct smile for the inverse pair (the foreign market). We first consider the case of two currencies and then the multi-currency setting. We illustrate the intermediate currency approach by applying it to the Heston and SABR stochastic volatility models, to the model in which exchange rates are described by an extended skewed normal distribution, and also to the model-free approach of option pricing