Please solve this problem in steps.

The course is Financial_Derivatives_and_Stochastic_Calculus

Problem 3 (40p) (Delta Hedging) Assume we are in a Black-Scheme world where on day t = 0 a stock is trading at 30 = $35 per share. The stock price volatility is or = 25% and it pays a continuous dividend yield D = 2%. Suppose the writer of a European option sells a call option with strike K = $33 on 1000 shares with time to expiration T = 180I days. Given risk-free interest rate r = 5% per annum, calculate the following (a) (ip) The call price and the corresponding delta at day 0. (b) [10p] The writer's trading strategy to maintain a delta-hedged portfolio on day I]. How much money does the writer need to borrow/ put in a risk-free money market on day 0 in order to maintain a delta-hedged portfolio? (c) (10p) The writer's prot if the stock price increases to $35.50 on day 1. Calculate also the cost to keep the portfolio delta neutral. (d) [10p] The writer's prot if the stock price falls to $34.80 on day 2. Calculate also the cost to keep the portfolio delta neutral. Note if Z w N (0, 1), then the cumulative standard normal distribution function in the range [0, x], :r > 0 can be approximated by 1 2:3 m5 x7 39 =_ __ ___ _