The interest rate with continuous compounding is r = 5% per annum. Under the real-world measure, the stock price (S) is given by S(t) = S0exp { + ()} WithS0 = 5, = 0.5, = 0.2.

(a) Find P(S(9) 5e) using N( ).

(b) We consider a European option with maturity T = 9 and payoff functionH(S) = { 1, > 5 0, 5 , (a so-called binary option). Write the option price V0 using an integral with (z).

(c) Evaluate the integral from (b) using N( ).