Markov-Functional Models with Local Drift

ArXiv ID: 2411.15053 “View on arXiv”

Authors: Unknown

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-Labordère (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.

Keywords: Local volatility models, Stochastic volatility interpolation, Term structure, Numerical algorithms, Markov-functional approach, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents advanced mathematical constructs involving stochastic differential equations, Markov-functional models, and quantitative finance theory with extensive use of formal proofs and complex equations, but it does not provide backtested results or implementation details for real-world data.

  flowchart TD
    A["Research Goal: Construct Local Volatility<br>Models from Discrete Marginal Distributions"] --> B["Methodology: Markov-Functional Approach<br>Extending Bass (1983) & Conze-Henry-Labordère (2022)"]
    B --> C["Data Inputs: Discrete Set of<br>European Option Marginal Distributions"]
    C --> D{"Computational Algorithm: Local Drift Construction"}
    D -- Case 1: Time-Homogeneous --> E["Step-Wise Time-Homogeneous<br>Local Volatility Structure"]
    D -- Case 2: Continuous Across Maturities --> F["Continuous Local Volatility<br>Across Maturities"]
    E --> G["Key Outcomes: Efficient Numerical Algorithms &<br>Parsimonious Term Structure Representation"]
    F --> G