Assume the following values when none is specified:

So $=100$

$\backslash$sigma $=20\%$ T$=1$ K $=100$ r $=5\%$Exercise $1-$ BSM PDE $-4\backslash$times $5$ points

$1.$ Using an explicit schema, what is the price of a call option, its delta, gamma and theta at inception?

Plot the values you get using different discretization steps.

$2.$ Using an implicit schema, what is the price of a call option, its delta, gamma and theta at inception? Plot the values you get using different discretization steps.

$3.$ Using a Crank$-$Nicolson schema, what is the price of a call option, its delta, gamma and theta at inception? Plot the values you get using different discretization steps.

$4.$ If you use the same discretization steps, which method performs the best $($compare with the values of exercise $0)$