Brazilian listed options with discrete dividends and the fast Laplace transform

Paper: arXiv 2212.01315

Authors: Maikon Araujo

Abstract

The Brazilian stock exchange (B3) has long used a strike-only adjustment to account for dividends in its listed equity options. This adjustment still makes it necessary to account for discrete dividends when pricing either calls or puts. This work presents a numerical procedure, based on the fast Laplace transform and its inverse, a procedure that can efficiently compute the Brazilian listed options’ premium and the Greeks delta, gamma, and theta with high accuracy.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically solid application of the fast Laplace transform to solve a specific regional market problem (B3 options with discrete dividends). While the numerical methods and mathematical formulations for option pricing and Greeks are rigorous, the empirical validation relies primarily on numerical accuracy tests rather than extensive historical market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Efficiently price B3 options <br>with discrete dividends & Greeks] --> B[Inputs: Spot, Strike-only adj., <br>Dividend amounts/dates, Volatility, Rates]
    B --> C[Methodology: Fast Laplace Transform <br>& Inverse FLT Numerical Scheme]
    C --> D[Compute Option Premiums <br>& Greeks: Delta, Gamma, Theta]
    D --> E[Key Findings: High accuracy, fast execution <br>& robust handling of Brazilian market rules]