Pricing time-capped American options using Least Squares Monte Carlo method
This paper develops a modified least squares Monte Carlo method to accurately price time-capped American options under Lévy processes.
What it examines
The paper introduces a modified Least Squares Monte Carlo method to price time-capped American options, particularly with drawdown-based termination, using geometric Lévy processes. It outlines the approach, algorithm modifications, and convergence proofs to efficiently value options with early exercise features under more general market models.
What it concludes
The results confirm that the modified LSMC method converges and accurately price time-capped options. The research has potential applications in risk management and pricing exotic derivatives, offering a robust tool for investors and practitioners while suggesting further investigation into model parameters and market scenarios.
Evidence objects
The paper innovatively extends the least squares Monte Carlo (LSMC) method for pricing American options with a time cap, terminating early upon specific events, thereby limiting risk and enhancing modeling.
key_findings bullet 1 · key_findings · validation V0
Authors propose a modified LSMC algorithm for pricing options with independent or asset-dependent caps, proving convergence as discretization shrinks and simulation count increases, with $$\text{geometric Lvy process}$$ yielding higher prices.
key_findings bullet 2 · key_findings · validation V0
The study offers robust algorithm design, detailed convergence proofs, and numerical comparisons of different cap settings, while noting that analysis of computational complexity in high-dimensional cases could enhance its impact.
key_findings bullet 3 · key_findings · validation V0
The paper adapts the Least Squares Monte Carlo method to price time-capped American options, integrating random time caps triggered by drawdown events in a Lvy market. Building on established techniques, the work offers original methodology with novel adaptations, providing practical insights that are compelling and valuable for practitioners and researchers.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
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 ou… ▽ More 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. △ Less
Source row: 1606 · abstract type: unknown