Using Terminal Stock Prices as Control Variates in Monte Carlo Estimation

Summary

The document asks how a terminal stock price can serve as a control variate when estimating a financial quantity by simulation. The question focuses on the control-variate adjustment: if the expected terminal price is known, the writer wonders whether subtracting it from the simulated price can improve an estimate, given that the realized terminal price is observed only at the end and no analytical stock-price solution is available.

No answer or empirical demonstration is included. The central issue is whether the control variable has a known expectation and is sufficiently correlated with the target quantity to reduce estimator variance; the simulated terminal price need not equal its expectation on each path. The document does not identify the paper, pricing model, or target payoff, so it cannot establish whether this particular control is effective. It serves as a conceptual question about applying variance reduction in Monte Carlo pricing.

Key ideas

• A control variate adjusts a simulated estimate using another quantity with a known expectation.
• The terminal stock price varies across simulation paths and need not equal its expectation on an individual path.
• Variance reduction depends on the control variable's relationship to the target quantity.
• The document asks about the method but supplies no answer or evidence of performance.

Tags

# Using stock prices as control variate


# Using stock prices as control variate












In this paper , the author suggested using terminal stock price as control variates. However, I do not understand as we only observe stock price distribution at the terminal, and we do not have any analytical solutions for the stock price, therefore E(F(a*) = F(a) + (S(T) - E(S(T))) and the last bit will always be the same (S(T) = E(S(T))), thus it does not provide correction for our estimate. Thank for any comments.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.