FRMEx_ans(11) - Financial Risk Management Jos Da Fonseca e...

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Financial Risk Management Jos´e Da Fonseca email: [email protected] Auckland University of Technology July-2012 Ex 1.8 : If you use put to hedge against a price decline then you will buy 50 puts. Because 1 put is written on 100 shares and you hold 5000 shares you need 50 = 5000 100 options. With respect to the strike you can take 25$ which is the current price. Ex 1.13 : 1. The holder of the option will make a gain if the stocks at maturity S T is such that S T > 52 . 5 . Because he will buy a stock paying 50 whereas on the market its price is S T > 52 . 5 , therefore he will earn at least 2.5$ which more than the premium or cost of the option paid at the beginning. 2. The option will be exercised whenever the stock ends above the strike which is equal to 50, ie S T > 50 . Remark that if the stock ends between 50 and 52.5 he will make a loss. 3. The profit diagram is given by a figure similar to Figure 1.3 (a) page 8. Ex 1.14 : 1. The holder of the option will make a gain if the stocks at maturity S T is such that S T < 56 . Because he will sell a stock receiving 60 whereas on the market its price is S T < 56 , therefore he will earn at least 4$ which more than the premium or cost of the option paid at the beginning. 2. The option will be exercised whenever the stock ends below the strike which is equal to 60, ie S T < 60 . Remark that if the stock ends between 56 and 60 he will make a loss. 3. The profit diagram is given by a figure similar to Figure 9.4 page 209 (for the diagram it is a short position which is asked). Ex 1.15 : wording aspect: “writing” an option means selling an option. 1. The writer of the option will have to pay 25 - 20 = S T - K = 5 but he received the premium at the beginning therefore his global position will be 2 - 5 = - 3 . Ex 1.20 : The trader wants to sell 100 million yen and receive dollars, it is a short position. 1. if the exchange rate at the end of the contract is $0 . 0074 per yen he will gain (0 . 008 - 0 . 0074)100000000 . 2. if the exchange rate at the end of the contract is $0 . 0091 per yen he will lose (0 . 0091 - 0 . 008)100000000 . Ex 1.27 : 1. We suppose that at maturity the stock can have 3 different values S T = 29 then his position will be - 2 . 75 + 1 . 5 . The options are not exercised. He paid 2 . 75 for the call with strike 30 and received 1.5 for selling the call with strike 32 . 5 . S T = 31 then his position will be 1 - 2 . 75 + 1 . 5 . The option with strike 30 is exercised which means that he will receive 31 - 30 = 1 . The other option will not be exercised. He paid 2 . 75 for the call with strike 30 and received 1 . 5 for selling the call with strike 32 . 5 . 1
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S T = 33 then his position will be 3 - 0 . 5 - 2 . 75 + 1 . 5 . The option with strike 30 is exercised which means that he will receive 33 - 30 = 3 . The other option will be exercised which means that he will have to pay 0 . 5 = 33 - 32 . 5 . He paid 2 . 75 for the call with strike 30 and received 1 . 5 for selling the call with strike 32 . 5 .
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  • Spring '14
  • Management, ex, USD, β, Auckland University of Technology

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