Smoothing discontinuities in option Greeks estimation: A sigmoid-family infinitesimal perturbation analysis approach

This paper addresses the estimation of option Greeks in the context of financial derivatives pricing and risk management. Although the classical infinitesimal perturbation analysis (IPA) method is favored for its ease of implementation and low variance, its application is severely limited by discontinuities in the payoff functions, such as those encountered in digital and barrier options. To address this challenge, we propose a sigmoid-family IPA (SF-IPA) method that uses a parameterized sigmoid function to smooth out discontinuities in the indicator function. This transformation yields an asymptotically unbiased derivative estimator with controllable bias. Theoretical analysis provides explicit non-asymptotic error bounds. Numerical experiments across various models demonstrate that the SF-IPA method achieves competitive performance in terms of both accuracy and efficiency.