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Xingyu Ren, Michael C. Fu, Pierre L'Ecuyer · 2026-06-25
The paper develops a new Monte Carlo method for estimating how the value of a financial model changes with respect to its parameters (sensitivities), even when the payoff has discontinuities. It improves an existing 'Leibniz derivative estimation' technique by adding a recursive conditioning step that removes the likelihood-ratio terms, which are the main source of high variance. Tested on an American call min-option, the new estimator shows lower variance and is simple to implement.
Why it matters: Accurate and stable sensitivity ('Greeks') estimates matter for hedging and risk management, especially for complex or path-dependent derivatives where standard Monte Carlo estimators can be noisy. A method whose variance doesn't blow up as the number of underlying inputs grows could be relevant to those pricing and hedging multi-asset or American-style options.
⚠ This is a methodological/simulation paper on a specific option model; results are theoretical and backtest-style, not evidence of trading profitability.
Leibniz derivative estimation is a Monte Carlo technique for estimating derivatives of a discontinuous sample performance in stochastic models with respect to parameters of interest. By combining the push-out likelihood ratio (LR) method with Leibniz integral rules, it generalizes a broad class of existing LR-based derivative estimators. However, as an LR-based method, its variance is often higher than that of perturbation analysis-based methods and may grow linearly with the dimension of the stochastic input whose distribution depends on the parameter. In this paper, we propose a recursive conditioning approach and combine it with the Leibniz derivative estimation framework. The resulting conditional Leibniz estimator does not involve LR terms and therefore is not subject to variance growth with the input dimension. It also has a simple form and is easy to implement. We apply the method to an American call min-option model, and simulation results show its effectiveness and low-variance performance.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.