Answer Happy

Barclays Ingliston Stock has a current price of $48. Its annual volatility is 28%. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3.5%. The volatility of the stock is 13%. The stock price follows the binomial models, with 24 periods, each of length 1 month. The continuously-compounded risk-free interest rate is 6% per annum. (i) Determine the price for a two-year at-the-money European call option on one share of this stock. (ii) Determine the price for a two-year at-the-money American put option on one share of this stock. (iii) Approximate the value of delta, gamma and theta at time 0 for a two- year at-the-money European call option on one share of this stock.