11. Suppose that the processes for S1 and S2 are given by these two equations: dS1= 1S1dt...

11. Suppose that the processes for S1 and S2 are given by these two equations:

dS1= α1S1dt + σ1S1dZ1 dS2 = α2S2dt + σ2S2dZ2 Note that the diffusions dZ1 and dZ2 are different. In this problem we want to find the expected return on Q, αQ, where Q follows the process dQ = αQQdt + Q

η1dZ1+ η2dZ2 Show that, to avoid arbitrage,

αQ

− r = η1

σ1

(α1− r) + η2

σ2

(α2 − r)

(Hint: Consider the strategy of buying one unit of Q and shorting Qη1/S1σ1 units of S1 and Qη2/S2σ2 units of S2. Finance any net cost using risk-free bonds.)