Asymptotic Equivalence Between Boundary Perturbations and Discrete Exit Times: Application to Simulation Schemes
We present two problems that are apparently disconnected, and we show how they are actually related to each other. First, we investigate the sensitivity of the expectation of functionals of diffusion process stopped at the exit from a domain, as the boundary is perturbed. Second, we analyze the discrete monitoring bias when simulating stopped diffusions, emphasizing the role of overshoot asymptotics. Then, we derive a simple and accurate scheme for simulating stopped diffusions.
KeywordsBrownian Motion Exit Time Euler Scheme Barrier Option Boundary Perturbation
This work has been partly done when the author was affiliated to Grenoble INP-Ensimag. The author is grateful to Grenoble Institute of Technology (BQR grant entitled Monte Carlo) and to the Chair Risques Financiers of the Fondation du Risque for their financial support.
The author also thanks the two referees for their valuable comments and suggestions.
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