please help me tackle this question appropriately

A non-dividend-paying stock, 5,, has a current price of 200p. After 6 months the price of the stock could increase to 230p or decrease to 170p. After a further h months, the price could increase from 230p to 250p, or decrease from 230p to 200p. From 170p the price could increase to 200p or decrease to 150p. The semi-annually compounded risk-free rate of interest is 6% per annum and the real-world probability that the share price increases at any time step is 0.75. Adopt a binomial tree approach with semi-annual time-steps. (i) Calculate the state-price deflator after one year. (5] (ii) Calculate, using the state-price deflator from (i). the price of a non-standard option which pays out max (0, log(S, - 180)} one year from now. (4] (iii) State how the answer to (ii) would change if the real-world probability of a share price increase at cach time step was D.6. [1] [Total 10] A non-standard derivative is written on a stock with current price S, = $2 and is exercisable at two dates, after exactly one year and at expiry, after exactly two years. If it is exercised at expiry it returns $1000 if and only if the stock price is below $2. If it is exercised after one year it returns $500 if and only if the stock price is above $2. Assume the market is a Black-Scholes one with a continuously compounded risk-free rate of 2%% per annum and a stock volatility of 30% per annum. (D) (a) Explain how the option should be priced after / - 1 (assuming that it is not exercised at / = 1). (b) Give an expression for the corresponding price, P.. 141 (ii) Denoting the price just after I year by p,4, explain why the fair price. p . at /= 1, is given by p1 = max(p1+, 500) if S, $2. [2] (iii) (a) Show that a holder should exercise the option at * = 1 if S, > k for a suitable value of A. (b) Calculate the value of A. [4] [Total 10]