A Resolution to Valuation Conflicts of Swaptions/Caps and OIS/LIBOR

Abstract

In this article, the authors provide a unified valuation framework under which a multicurve economy can be established and caps/floors and swaptions can be consistently priced. Furthermore, if a lognormal distribution is employed for the forward price (or 1 plus forward rate), then a “model-free” volatility calibration can be achieved, and all swaptions and caps/floors are perfectly repriced.

This article leverages earlier work by Chen, Hsieh, and Huang (2017) who fix a crucial drift-adjustment problem of the traditional LIBOR market model (LMM) where the LIBOR rates follow a lognormal distribution. By assuming 1 + LIBOR to be lognormal (hence LIBOR is shifted lognormal), Chen, Hsieh, and Huang achieve an exact and deterministic drift-adjustment term. In this article, they extend the model to provide a perfect calibration to both swaptions and caps/floors (which is not doable under the traditional LMM), and by using a foreign currency analogy, they show that the model supports multiple curves, which is a key element to overnight index swap (OIS) discounting.