FIN2020 Homework 7

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FIN2020 Homework 7

Prices of Contingent Claims and Complex Assets:

Consider an economy in which there are two dates t= 0 and t = 1, and two possible states, i= 1 and i=2, at t= 1, which occur with equal probability, so that m1 == 1/2. In this economy, two "complex" assets are traded. The first sells for price P = 2 at t = 0 and makes payoffs of 2 =2 in state i = 1 at t = 1 and 2 = 4 in state i = 2 at t = 1. The second sells for P = 1.25 at t = 0 and makes payoffs 22 = 1 in state i = 1 at t = 1 and Z2 = 3 in state i = 2 at t = 1.

a. Use this information to compute the price q at t = 0 of a contingent claim that pays off one in state i = 1 at t = 1 and zero in state i = 2 at t = 1 and the price q2 at t = 0 of a contingent claim that pays off zero in state i = 1 at t = 1 and one in state i = 2 at t = 1.

b. Use your answers from part (a), above, to compute the price P at t 0 of a bond that pays off =1 in state i =1 at t = 1 and Z =1 in state i = 2 at t = 1.

c. Use your answers from part (a), above, to compute the price P at t = 0 of a share of stock that makes no dividend payments, but can be sold for P = 2 in state i = 1 at t = 1 and P? =3 in state i = 2 at t = 1.