MA320-6-SP 1. (a) Just before the market closing time on a given day, you lose access to the share prices, but some European call and put prices are available as follows: strike price call price put price $75 $11 $3 $85 $7 $8 $95 83 If all the options have the same expiration date and no dividends are paid, then evaluate the price of the $95 strike European put option. [4 marks] (b) A one-year forward contract on a share was agreed on 1 March 2020, when the share price is 78 and the continuously compounded risk-free rate was 14% per annum. This share is expected to pay dividends of 3.20 on 1 June 2020, and 1 December 2020. On 1 April 2020, the share price is 80 and a continuously compounded risk-free rate is 11% per annum. Calculate the value of the contract to the holder of the long forward position on 1 April 2020. [6 marks] [Total marks 10 5. Consider a two-period binomial model for a non-dividend-paying share whose current price is S= 100. Over each six-month period, the share price can either move up by a factor u 1.2 or down by a factor of d-0.8. the risk-free rate is r 5% per six-month period. (a) Prove that there is no arbitrage in the market. [2 marks] [2 marks] (b) Construct the binomial tree of share prices. (c) Calculate the price of a European call option written on the share with [3 marks] a strike price K= 100 and maturity of one year. (d) Consider a modified call option based on the above parameters. In this case, the underlying asset price at maturity is the arithmetic average of years. That share prices, denoted Ar, at times 0, 0.5 and 1 measured in is, the payoff at maturity is given by mar (Ar-100,0). Calculate the initial price of this call option, assuming it can only be [3 marks] exercised at maturity