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1) People usually consider an instantaneous covariance while you are considering a integrated covariance. In a model $$ dS_t = S_t \cdot (\alpha(t)dt + A(t)dW_t) $$ the integrated covariance of log-returns is simply the integral over time of the instantaneous covariance: $$ Cov(R_i(t),R_j(t)) = (i,j)\textrm{-coeff. of} \int_0^t \underbrace ...



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