1. The price of a US stock and the exchange rate Dollar/Euro are given by, with W₁ having correlation p with W₂, dS(t)/S

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1 The Price Of A Us Stock And The Exchange Rate Dollar Euro Are Given By With W Having Correlation P With W Ds T S 1 (94.64 KiB) Viewed 34 times

1. The price of a US stock and the exchange rate Dollar/Euro are given by, with W₁ having correlation p with W₂, dS(t)/S(t) = µdt + odW₁(t) dQ(t)/Q(t) = Bdt + ddW₂(t) (i) Find the Brownian motions W₁ and W₂ such that the discounted dollar value of the euro bank account e-rtQ(t)erft is a martingale, and the discounted dollar value of the domestic stock e-t S(t) is also a martingale under the corresponding probability P*, where r and rf are the US and the Euro risk-free interest rates, respectively. (ii) Find the domestic price of the payoff of C(T) = log(Q³(T)S³ (T)) dollars.