Consider a bull spread where you buy a $40-$strike put and sell a $45-$

strike put. Suppose $\backslash$sigma $=0\mathrm{.}30,$ r $=0\mathrm{.}08,\backslash$delta $=0,$ and T $=0\mathrm{.}5.$ Use

the excel spreadsheets when you compute gamma and vega. Use the

normal table when you compute delta.

a$.$ Suppose S $=40.$ What are delta, gamma, and vega?

b$.$ Suppose S $=45.$ What are delta, gamma, and vega?

c$.$ Consider a bull spread when you buy a $40-$strike call and a $45-$

strike call. Repeat $($a$)$ and $($b$).$ You can refer the answer key of

Exercise $11\mathrm{.}14$ of the text book. Compare the results with the

result of $($a$)$ and $($b$)$ above. Which greeks are identical? Why are

they identical?