FX Vanilla Pricing and Smile Calibration

Abstract

The first part of this document is dedicated to the pricing of undiscounted Vanilla Options: we compute the price and sensitivities of Calls and Puts, and highlight the different FX Delta conventions. The most important application of specific FX market conventions (and particularly Deltas conventions) is the FX smile construction. Indeed, the way the smile is described in forex market radically differs from other asset classes (equity, commodity...), requiring a specific procedure to recover the smile as a function of strike. In the second part of this document, we present two different approaches for the construction of one smile maturity slice. We apply both approaches to the calibration of UsdJpy 6 Months maturity smile and discuss the results.

Keywords: Fx Conventions, Market Strangle, Fx Smile Calibration, SVI volatility

JEL Classification: G13