Econometric Identification of Foreign Exchange Options Volatility Surfaces Recovering Foreign Exchange Option Prices from Spot Price Dynamics

Abstract

Over-the-counter foreign exchange options are the fourth largest derivatives market (by asset class) in the world, but this market is little studied in the finance literature. We propose a new set of modelling tools for pricing options on this market and demonstrate their applicability to five liquid currencies versus the dollar. Our discrete time affine nested GARCH based model specification is the first of its type to be estimated directly from spot foreign exchange and short rate (timed deposit) quotes. Out-of-sample testing suggests that an affine term structure with stochastic volatility model estimated at a monthly frequency outperforms most specifications with no recourse to option market quotes to assist calibration. Indeed, this model outperforms a realized variance model by almost an order of magnitude, across all quote types, when compared to observed option market data.