Markov-Functional Models with Local Drift

ShengQuan Zhou

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arXiv · 2411.15053

Markov-Functional Models with Local Drift

ShengQuan Zhou

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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.

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ShengQuan Zhou. 2024-11-22. Markov-Functional Models with Local Drift. https://arxiv.org/abs/2411.15053

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