Pricing European option if Stock price follows a normal distribution

Suppose the stock price S obeys a normal (instead of a lognormal) distribution: Sr ~ N(SoerT, OVT) We'd like to calculate the price of an option which pays max(S7 - K,0) at expiry T. The way to do it is to calculate the following expectation value: 1 C = e-T E[max(S K,0)] = e- ***J max(Sge"" +oVx K,0) e *dx =e="[" (Sher +oV7x-K) *dx V21 V21 K SoerT Where d = OVT Your task is to find the option price by solving the above integral. = Hint: you can express your final answer with the following function: N(z) vi let'de 0o 1 -X Notice that N(-2) = 1 N(z) S 72 e 2 dx V2r Z Suppose the stock price S obeys a normal (instead of a lognormal) distribution: Sr ~ N(SoerT, OVT) We'd like to calculate the price of an option which pays max(S7 - K,0) at expiry T. The way to do it is to calculate the following expectation value: 1 C = e-T E[max(S K,0)] = e- ***J max(Sge"" +oVx K,0) e *dx =e="[" (Sher +oV7x-K) *dx V21 V21 K SoerT Where d = OVT Your task is to find the option price by solving the above integral. = Hint: you can express your final answer with the following function: N(z) vi let'de 0o 1 -X Notice that N(-2) = 1 N(z) S 72 e 2 dx V2r Z