Assume the following values when none is specified:

So $=100$

$\backslash$sigma $=20\%$ T$=1$ K $=100$ r $=5\%$

We will add another stock to the mix with the following characteristics:

Xo $=90\backslash$sigma $=30\%$

Assume the correlation

$\backslash$rho $=50\%$

We want to value a spread option whose payoff is max$($ST $$ XT $$ Kspread, $0)$ with Kspread $=8$

$1.$ UsingaMonteCarlomethodofyourchoice,whatistheprice,delta,gammaandthetaofthisderivative? $2.$ Plot how the price changes with different values of the correlation? Any intuitive explanation?