Pricing time-capped American options using Least Squares Monte Carlo method

Paper: arXiv 2503.01040

Authors: Paweł Stȩpniak, Zbigniew Palmowski

Abstract

In this paper, we adopt the least squares Monte Carlo (LSMC) method to price time-capped American options. The aforementioned cap can be an independent random variable or dependent on asset price at random time. We allow various time caps. In particular, we give an algorithm for pricing the American options capped by the first drawdown epoch. We focus on the geometric Lévy market. We prove that our estimator converges to the true price as one takes the discretisation step tending to zero and the number of trajectories going to infinity.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous theoretical modification of the Least Squares Monte Carlo (LSMC) algorithm for pricing time-capped American options in a Levy market, including formal convergence proofs. While it includes numerical analysis, the primary strength lies in its mathematical formulations and adaptation of optimal stopping frameworks.

Research Flowchart

  flowchart TD
    A[Research Goal: Price Time-Capped American Options via LSMC] --> B[Inputs: Geometric Lévy Market & Time Caps]
    B --> C[Time-Cap Scenarios: Random Variable or First Drawdown Epoch]
    C --> D[Computational Process: Discretization & LSMC Algorithm]
    D --> E[Convergence Proof: Timesteps to 0, Trajectories to Infinity]
    E --> F[Outcome: Convergent Estimator for Time-Capped Option Prices]