Derivation of the closed-form formulas for European options Let DT = max(0, ST – K) be the payoff of a European call with strike K and maturity T. The following questions provide a step-by-step derivation of the closed-form formulas for c0 and p0 in the lognormal model.
(a) Show that 
where 
and 
otherwise.
(b) Show that ST has the same distribution as 
(c) Show that Y > K if and only if 
(d) Using the change of variable 
, show that 
.
(e) Establish the closed-form formulas for c0 and p0.
