Estimating security price derivatives using simulation
Management Science
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Kernel Estimation of the Greeks for Options with Discontinuous Payoffs
Operations Research
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Monte Carlo simulation has been widely used as a standard tool for estimating expectations. In this paper we develop a variance reduction technique for a particular case when the expectation is taken under a constraint that a sum of random variables is larger than a threshold. The proposed technique is based on a reflection argument on the sample space and requires knowing the joint density of the random variables. It turns out the technique can always guarantee a variance reduction. More importantly, the technique sheds light on how observations violating the constraint can be used more efficiently in estimation, compared to crude Monte Carlo.