Financial Mathematics

QUESTION 4 Let S be the price of a non-dividend paying share, and let r be the continuously compounded risk-free rate (a) Let K be the forward price and T the time to maturity. Consider the following portfolios: - A: one long forward contract - B: borrow Ke(rT) cash and buy one share at S0. What is the values of both portfolio at T? [3] Using the principle of no arbitrage, derive the forward price at time zero for the forward contract on S with maturity T. [4] Assume that, at time zero, the share price is 500, and that the forward contract has maturity two years. The share pays a dividend of 5% of the share price every six months with the next dividend due in two months, and the continuously compounded risk-free rate is 3% p.a. b) Determine the forward price for this contract. [3] Hint: consider two portfolio similar (i) but include the dividend as well