A Two-Step Longstaff Schwartz Monte Carlo Approach to Game Option Pricing

ArXiv ID: 2401.08093 “View on arXiv”

Authors: Unknown

Abstract

We proposed a two-step Longstaff Schwartz Monte Carlo (LSMC) method with two regression models fitted at each time step to price game options. Although the original LSMC can be used to price game options with an enlarged range of path in regression and a modified cashflow updating rule, we identified a drawback of such approach, which motivated us to propose our approach. We implemented numerical examples with benchmarks using binomial tree and numerical PDE, and it showed that our method produces more reliable results comparing to the original LSMC.

Keywords: Longstaff Schwartz Monte Carlo, Game Options, Regression Models, PDE Pricing, Binomial Tree, Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces advanced mathematical modifications to the Longstaff-Schwartz Monte Carlo method, involving two-step regressions and basis function selection, which increases mathematical density. However, empirical testing is limited to theoretical benchmarks (binomial tree and PDE) without reported real-world data, out-of-sample performance metrics, or executable code, placing it in the theoretical research quadrant.

  flowchart TD
    A["Research Goal: Price Game Options"] --> B["Problem: Original LSMC Drawback"]
    B --> C{"Two-Step LSMC Method"}
    C --> D["Step 1: Path Generation"]
    C --> E["Step 2: Two Regression Models"]
    D --> F["Monte Carlo Simulation"]
    E --> F
    F --> G["Binomial Tree & PDE Benchmarks"]
    G --> H["Key Finding: Reliable Results"]
    style A fill:#e1f5fe
    style H fill:#e8f5e8