Midterm_2006 - Hagfri og strfri fjrmlamarkaa 04.07.50...

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Hagfræ ð i og stær ð fræ ð i fjármálamarka ð a 04.07.50 Mi ð annarpróf 4. nóvember 2006 kl. 10 – 13 1. Gefi ð er CRR líkani ð me ð 1 T = , 10% r = , ( ) 0 100 S = , 1,2 u = , 0,8 d = . Settu saman ver ð bréfasafn úr S og B sem líkir eftir kauprétti á S me ð 110 K = . Hvert er ver ð kaupréttarins vi ð tímann 0 t = ? 2. Gefi ð er MBS líkani ð me ð 0 r = og ( ) 0 105 S = . S ý ndu a ð fyrir evrópska kaup- og sölurétti me ð 95 K = gildir ( ) ( ) 0 0 10 c p = + . 3. Nota ð u reglu Itos til a ð finna slembna diffurjöfnu fyrir 4 W þ ar sem W er Brownsk hreyfing. Ger ð u þ a ð sama fyrir 0,5 S þ ar sem S er hlutabréfaver ð i ð í MBS líkaninu. 4. Íslenskur i ð nrekandi hefur gert samning um kaup á framlei ð slutækjum frá Bretlandi. Tækin ver ð a afhent eftir 3 mánu ð i og i ð nrekandinn vill gera framvirkan samning um kaup á sterlingspundum (GBP) sem tryggir honum fast gengi. Vextir á áhættufríum bréfum í íslenskum krónum (ISK) eru 15% á ársgrundvelli en í GBP eru vextirnir 5%.
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