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You most probably don't want to estimate the covariance of prices but rather the covariance of returns. Thus for equities you can take the return of the traded price. For bonds: if the maturity is long enough (say bigger than 2 years), then you can take the returns of traded prices. The pull to par should not be too relevant here. if the maturity is short ...


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The first objective is to minimize the variance by choosing a proper control variate. First note that an expectation value is just a constant, so the covariance between an expectation value and a random variable is zero: $$\text{Cov}\left(\mathbb{E}[Y], X\right) = 0$$ Similarly for the variance of an expectation value, $\text{Var}(\mathbb{E}[Y])=0$. The ...



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