3952 page 1 of 3 if st k stat 473 hw 1 solution 3 c

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Unformatted text preview: TAL 0 $ 1.3952 $ 1.3952 ! ! If S(T) > K ! The profit after one year = $ 1.3952! Page 1 of 3 If S(T) < K STAT 473! HW 1 Solution 3.! ! C ( K , T ) − P ( K , T ) = S0 − PV ( Div ) − K ⋅ e− rT ! ! ! ! Notice that the second dividend is 9 months from today,! but the agreement period is only 6 months.! Therefore, the 9-month dividend is irrelevant in this question.! ! C ( K , T ) − P ( K , T ) − S0 + K ⋅ e ! 9 − 5 − 100 + 99 ⋅ e 2 −r 4 ! ! ! 4.! 6 − r⋅ 12 = 2⋅e − rT = PV ( Div ) = 2 ⋅ e 1 −r 4 3 − r⋅ 12 ! 1 −r 4 99 ⋅ e − 2 ⋅ e = 96 ⇒ r ≈ 2.0514% Hint: Substitute x = e − r 4 to solve the equation! C ( K , T ) − P ( K , T ) = S0 ⋅ e−δ T − K ⋅ e− rT 40 − 25.33 = 1000 ⋅ e−δ ×1 − 1040 ⋅ e−12%×1 ! 1000 ⋅ e−δ = 40 − 25.33 + 1040 ⋅ e−12%×1 ≈ 937.0673 ! e−δ = 0.9370673 ! 5.! ! ! δ = − ln ( 0.9370673) ≈ 6.5% Part (a)! C ( K , T ) − P ( K , T ) = S0 − PV ( Div ) − K ⋅ e− rT 1.90 − 1.00 = S0 − 1 ⋅ e ⇒ S0 ≈ 45.3410 − 3 ×...
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This document was uploaded on 02/17/2014 for the course STAT 473 at Purdue University-West Lafayette.

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