4. Suppose that S1 and S2 follow geometric Brownian motion and pay continuous proportional dividends at the
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4. 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 S1(t)e
−δ1(T−t)N ln(S1(t)/KS2(t)) + (δ2 − δ1+ 0.5σ2)(T − t)
σ
√
T − t
where σ2 = σ2 1
+ σ2 2
− 2ρ1, 2σ1σ2 and δ1 and δ2 are the dividend yields on the two stocks.
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Related Book For
Derivatives Markets Pearson New International Edition
ISBN: 978-1292021256
3rd Edition
Authors: Robert L. Mcdonald
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