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1

Indeed Pearson correlation coefficients measure only linear relationships. Spearman correlation coefficients measure only monotonic relationships There is a comprehensive article there.


1

Best-of + Worst-of = Call1 + Call2 The right hand side is independent of correlation (and you can check it in your model). Therefore if Best-of is short correlation, worst-of must be long correlation. Increasing correlation makes the two assets more similar and therefore makes the best-of more like a vanilla. This is why a best-of is short correlation. (Hope ...


3

Intuitively, they should both be short correlation, that is the less correlated the assets are the higher the value of the worst of/best of option. The best of option payoff is sandwiched by an exchange option payoff (plus other vanilla forward/option payoffs on single stock, insensitive to correlation): $$ X_T -K + (Y_T-X_T)^+ \leq \max(X_T - K ,Y_T - K,0) \...


2

Note that \begin{align*} \left\langle \int_0^t \sigma_s^1 dW_s^1, \int_0^t \sigma_s^2 dW_s^2\right\rangle &= \int_0^t \sigma_s^1 \sigma_s^2 d\langle W_s^1, W_s^2 \rangle\\ &=\int_0^t \rho_s\sigma_s^1 \sigma_s^2 ds. \end{align*}


0

Since the correlation matrix is symetric, if you move the term (i,j), you have to do it for the term (j,i) as well Of course -> the correlation of an asset with itself is equal to 1... so it should not change You apply a downward shock (1 to 0.99) and you use the formula of finite differences


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