Question 2 Corsider the followina ins. mrvn stands for megawat hour, it is the unin to measure a quancty of electricty. All options have size of 1 MWh. For instanoe, the paycif at erpiry of a long position in the at expiry. The fo-year risk-treo interest rate is 0 . a) Which combination of options have the following payoff at expiry lanere the option premiums paidirecetved at \\( (t-0) \\) : cothes poyot at eying Ifndicate clearly the number and direction of each of option position. For instance, write: \" 1 short position in call \\( (K=40)+2 \\) long positions in put (K-50)? (5 marks) You develop a new type of power plant, which will be able to produce electricity in 10 yoars. In 10 years' time, when the plant is ready to work you will ssill have the choice of whether to produce or not. You will have the choice between: - producing 100 milion MWh of electricity at a production cost of 40 6MWh: - or not producing anything at zero production costs. After that, the plant will be out-of-order (whether you produce or not), that is, the only date at which electricity can be produced is at \\( t=10 \\) years. Question 2 continues on the noxt page:... b) Which option position should you take in order to be perfectly hedged, that is, to eliminate all uncertainty about your total payoff at \\( t=10 \\) years? [Indicate clearly whether you take long/short positions in calls/puts and with which strike price.] (5 marks) c) Developing the new power plant costs \\( X \\) to be paid today. At which condition on \\( \\mathrm{X} \\) is the development of the new power plant a positive Net Present Value investment? Show your calculation. (5 marks) Suppose in the next question that the 10 -year risk-free interest rate is \0, the call option with strike price \\( \\mathrm{K}=60 / \\mathrm{MWh} \\) trades at a premium \\( \\mathrm{C}_{0}=3 \\) and the put option with strike price \\( \\mathrm{K}=60 / \\mathrm{MWh} \\) trades at a premium \\( \\mathrm{P}_{0}=11 \\). d) What is an arbitrage strategy that involves lending/borrowing at the risk-free rate and positions in the call and put options with strike prices \\( K=50 \\) E/MWh and \\( K=60 / M W h \\) ? [ndicate clearly the composition of the strategy. For instance, write: \"Borrow \\( 5 +1 \\) short position in call \\( (K=50)+1 \\) long positions in put \\( (K=60) \\) \". You are not asked to show the cash flow.] (10 marks)