# quantitative finance

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Student’s name Teacher’s name Student’s group 01 February 2018 Problem-solving Problem (a) The expected value of the unhedged firm is: 0.5*200/(1+0.05)+0.5*(500-(500-300)*0.4)/(1+0.05)=95.24+200=295.24 Problem (b) Let’s buy put options for gold pricing at 500 with premium P. The expected value of the hedged firm is: (500-(500-300)*0.4)/(1+0.05)-P=420-P Problem (c) The safe debt is the one that pays off not more than 200 in a year. The value of the firm is:0.5*(200-200)/(1+0.05)+0.5*(500-200-(500-200-300)*0.4)/(1+0.05)=142.86 Problem (d) The safe debt is the one that pays off not more than 200 in a year. Let’s buy put options for gold pricing at 500 with premium P. The value of the firm is: (500-200-(500-200-300)*0.4)/(1+0.05)-P=285.71-P Problem (e) The firm’s value is: 0.5*(200-250-20)/1.05+0.5*(500-250)/1.05=119.05-33.33=85.71 The return of the investment may be either: -(33.33/250)=-13.3%, or 119.05/250=47.6% The yield to maturity is: ytm=((0.05+0.5*(-0.133-0.05))+ (0.05+0.5*(0.476-0.05))/2=(-0.0415+0.263)/2=11.1% Problem (g) We have 2 scenarios for each case:value 200 and no gamble – expected result is 200-250-20=-70 Value 200 and gamble: unlucky gamble=200-250-20-20=-90, lucky gamble:200-250+1000-(1000+200-250-300)*0.4=690 Expected result is: 0.005*690-0.995*90=-86.1 Equity holders will choose not to gamble Value 500 and no gamble – expected result is 500-250=250 Value 500 and gamble: unlucky gamble=500-250-20=230, lucky gamble:500-250+1000-(1000+500-250-300)*0.4=870 Expected result is:0.005*870+0.995*230=233.2 Expected YTM in case a is -20%, in case b – 100%. Problem (h) In case of hedging there are 2

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