Modelling and analysis of financial instrument

Question 2. Assume that the risk-free interest rate is 2.5% per year. Set up an Option strike price K at 110%x share price on the first day's trading of Jan 2023, rounded up to the nearest 10p. For example, if that closing price were 240p then 1.1240=264 which results in K=270p, rounded up to the nearest 10p. The share price on the first day's trading of Jan is 4713 pence. a) Determine the price on the first day's trading of Jan 2023 of a European Put option on your share, maturing in 6 months at the strike price K calculated above, using the Black-Scholes pricing formula. Use the annualized volatility of 31.87% for your share. Use a calculator, Statistical Tables and show your work. (You should check your answer with Excel but there are no marks for reporting Excel calculations for this question or for part (b) below) b) Suppose your share issues annual dividends of 5\%, payable in 3 months' time (end of March 2023). Determine the price on the first day's trading of Jan 2023 of a European Put option on your share, expiring in 6 months using the same strike price K and volatility as in Q2a), by using the dividend-adjusted Black-Scholes formula. Use a calculator, Statistical Tables and show working. c) Assume that you are a trader and have sold 10 Put options priced as in Q2a) above. How would you Delta hedge your exposure on this contract? How would your hedge be managed over the 6 months until the exercise date? d) Use the bounds on the price of an American Put Option and compute a price range for this American Option using the same contract data as above in Q2a). How does the American price range compare to the European Put price