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Markov-Functional Models with Local Drift

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  • ShengQuan Zhou

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. "Markov-Functional Models with Local Drift," Papers 2411.15053, arXiv.org.
    • Handle: RePEc:arx:papers:2411.15053
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    References listed on IDEAS

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    1. Noble, John M., 2013. "Time homogeneous diffusions with a given marginal at a deterministic time," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 675-718.
    2. Hadrien De March & Pierre Henry-Labordere, 2019. "Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants," Papers 1902.04456, arXiv.org, revised Jul 2023.
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