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Another approach as follow. The $T$-Straddle option $X$, i.e. X=\left\{ \begin{align} & K-S(T)\quad ,\quad 0<S(T)\le K \\ & S(T)-K\quad ,\quad S(T)>K \\ \end{align} \right. has then following contract function \Phi (x)=\left\{ \begin{align} & K-x\quad ,\quad 0<x\le K \\ & x-K\quad ,\quad x>K \\ \end{align} \right.... 3 just take a call and a put struck at K and add them together. For the hedge just add the hedges together as well. 0 That's the risk that MM's take, generally. This is commonly referred to as "gap risk". Holistically the idea is that with the law of large numbers you will lose sometimes but overall be OK as you have a large number of these trades. On our MM desk we have seen a few times where big takeovers were preceded by someone in the market lifting 10k call ... 0\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 $$AS a result, you should borrows 1.36 at time zero and buys the put ... 0 Several issues arise no matter which approach you choose (as a reference for my claims you can go through this: the covariance matrix of many assets can become instable (the more assets the more instable). Then your PCA will be based on noise. Therefore first get a good stimator of covariance. Using data of something like a year of observations worked good ... 2 Just a heads up, I'm not going to go through all the mathematical caveats of using this approach. Let \Sigma be your covariance matrix, and X a random vector of daily returns. So$$\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 ...