Suppose that S1 and S2 follow geometric Brownian motion and pay continuous proportional dividends at the rates δ1 and δ2. Use the martingale argument to show that the value of a claim paying S1(T ) if S1(T) > KS2(T ) is

where σ2 = σ2 1 + σ2 2 ˆ’ 2ρ1, 2σ1σ2 and δ1 and δ2 are the dividend yields on the two stocks.

Transcribed Image Text:

In(S,(t)/K S2(t))+ (82 – 81 + 0.50?)(T - t)' S;(t)e-d1(T–4)N oVT-t