medium · Quantitative Finance
When using Monte Carlo to price an arithmetic Asian option, a practitioner uses the payoff of a geometric Asian option as a 'control variate'.
What is the primary requirement for this technique to be effective?
- The geometric leg need not pay more than the arithmetic leg; on average its payoff is actually lower, not higher.
- Using a wholly different underlying asset severs any correlation, which defeats the entire purpose of the control variate.
- Drawing the control variate from a separate random seed removes the shared-path error the whole variance-reduction mechanism relies on.
- The geometric Asian option must have a known closed-form solution and be highly correlated with the arithmetic payoff.
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