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$$\Delta_1(H)=\frac{V_2(HH)-V_2(HT)}{S_2(HH)-S_2(HT)}=-\frac{1}{12}$$ and $$\Delta_1(T)=\frac{V_2(TH)-V_2(TT)}{S_2(TH)-S_2(TT)}=-1$$ and $$\Delta_0=\frac{V_1(H)-V_1(T)}{S_1(H)-S_1(T)}=-0.433$$ The optimal exercise time is $$\tau(HH)=\infty $$ $$\tau(HT)=2 $$ $$\tau(TH)=1 $$ $$\tau(TT)=1 $$ AS a result, you should borrows $1.36$ at time zero and buys the put ...


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Several issues arise no matter which approach you choose (as a reference for my claims you can go through this: the covariance matrix of many assets can become instable (the more assets the more instable). Then your PCA will be based on noise. Therefore first get a good stimator of covariance. Using data of something like a year of observations worked good ...


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Just a heads up, I'm not going to go through all the mathematical caveats of using this approach. Let $\Sigma$ be your covariance matrix, and $X$ a random vector of daily returns. So $$\text{Var}(X) = \Sigma.$$ You have a bug in your code. In your code you call it pxCov, but you probably meant to use cov() insted of cor(). Check out the documentation to ...



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