Markov-Functional Models with Local Drift

TL;DR

This paper presents a novel Markov-functional approach for constructing local volatility models calibrated to specific marginals, extending previous interpolation methods and providing efficient algorithms for different volatility function scenarios.

Contribution

It introduces a new Markov-functional framework that extends existing volatility interpolation techniques and offers practical algorithms for model construction.

Findings

Efficient numerical algorithms for local volatility functions.

Time-homogeneous and continuous volatility models demonstrated.

Parsimonious local volatility term structure representation.

Abstract

We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and Henry-Labord\`ere (2022). The method is illustrated with efficient numerical algorithms in the cases where the constructed local volatility functions are: (1) time-homogeneous between or (2) continuous across, the successive maturities. The step-wise time-homogeneous construction produces a parsimonious representation of the local volatility term structure.