Good post.

A question on the equity turbulence – did you use the S&P 500 constituents in calculation of the turbulence? Because the turbulence index requires cross-mean and covariance matrix.

Thanks! ]]>

Prices are always greater than zero. p>0. Hence, modelling them with geometric stochastic motion is appealing.

dp = p*r*dt+p*b*dW, guarantees p > 0 (if p_0 > 0), and the solution is log-normal prices.

If instead we chose dp = r*dt + b*dW, p can be anywhere on the reals, which isn’t realistic.

There are other choices that guarantee positive definiteness too, and which are perhaps better suited to modelling prices.

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