1.A company's current stock price is S₀ = 100, and it is assumed that in the future it will follow the geometric Brownian motion given by dS_t = 0.10S_tdt + 0.20S_tdw_t, where w_t denotes Brownian motion.

a.Express Pr[S₁>120] in terms of a probability statement on the standard normal z~N(0,1).

b.The risk free rate is 0.02. What is the price of a 1-year binary call option on this company, that pays $100 if S₁>120? You can leave this answer in terms of a probability statement on z~N(0,1).