Incorporating a Volatility Smile into the Markov-Functional Model

TL;DR

This paper enhances the Markov-Functional interest-rate model by integrating a volatility smile through UVDD digital mapping, enabling better pricing, smile prediction, and hedging of Bermudan swaptions.

Contribution

It introduces a UVDD-based digital mapping into the MF model to incorporate the volatility smile, improving pricing accuracy and hedge performance.

Findings

The model accurately prices Bermudan swaptions.

It predicts future implied volatility smiles.

Hedging simulations show improved performance.

Abstract

We study a Markov-Functional (MF) interest-rate model with Uncertain Volatility Displaced Diffusion (UVDD) digital mapping, which is consistent with the volatility-smile phenomenon observed in the option market. We first check the impact of pricing Bermudan swaptions by the model. Next, we also investigate the future smiles implied by the MF models and the smile dynamics implied by the UVDD model. Finally, we conduct hedging simulations against Bermudan swaptions to test extensively the hedge performance of this smile-consistenet MF model.