Multi-asset and generalised Local Volatility. An efficient implementation

ArXiv ID: 2411.05425 “View on arXiv”

Authors: Unknown

Abstract

This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local volatility.

Keywords: Hybrid Numerical Method, Option Pricing, Local Volatility, Stochastic Drift, Monte Carlo Simulation, Equity and Interest Rate Hybrids

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents a novel hybrid numerical method (ODgrid) involving advanced mathematical concepts like generalized diffusions, Fokker-Planck, and cubic interpolation, but it also includes a specific implementation pseudo-code and a calibration table comparing market implied volatilities with model output, indicating significant empirical implementation considerations.

  flowchart TD
    A["Research Goal: Efficient Pricing of Multi-Asset<br>and Generalised Local Volatility Options"] --> B["Methodology: Hybrid Numerical Method"]
    B --> C{"Key Inputs & Assumptions"}
    C --> D["Stochastic Processes:<br>Asset Prices, Local Volatility, Stochastic Drift"]
    C --> E["Market Data: Correlation &<br>Interest Rate Curves"]
    D --> F["Computational Engine:<br>Advanced Monte Carlo Simulation"]
    E --> F
    F --> G["Key Findings & Outcomes"]
    G --> H["Accurate Pricing for Equity/IR Hybrids"]
    G --> I["Efficient Handling of<br>Multi-Asset & Local Vol Models"]