Paper: arXiv 2411.05425

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]