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Midterm Solutions_2008

Midterm Solutions_2008 - Hagfri og strfri fjrmlamarkaa...

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Hagfræ ð i og stær ð fræ ð i fjármálamarka ð a Lausnir vi ð mi ð annarprófi 2008. 1a) put: C=(K-S(1)) + i. 0 (1+0,18) + 1 120 = (90-120) + = 0 ii. 0 (1+0,18) + 1 80 = (90-80) + = 10 Í subtract equation ii. From equation i. and get: 1 120 - 1 80 = -10 => 1 = -0,25 => 0 (1+0,18) + -0,25*80 = 10 => 0 = 25,424 I take a short position of 0,25 shares of S(t) and deposit 25,424 in the bank. Arbitrage free price is therefore C=25,424 + -0,25*100= 0,424 1b) t=0: The Bank writes the put at 0,424 and takes a short position of 0,25 shares, sells the shares and deposits 25,424 in the bank. t=1: a. If the price goes up to 120 then he buys 0,25 shares @30 with the deposit in the bank which now has become 25,424*1,18=30 and then delivers the shares to close the short position. b. If the price goes down to 80 then he buys 0,25 shares @20 with the deposit in the bank and pays the 10 to the owner of the put and then delivers the shares to close the short position. Net cashflow at t=1 is therefore zero for the two scenarios and the arbitrage free price is therefore 0,424.
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