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Consider two exchange rates X/Y and Z/Y. (For example EUR/USD and JPY/USD.) They both follow perfectly correlated geometric Brownian motions with parameters (1, 1) and

Consider two exchange rates X/Y and Z/Y. (For example EUR/USD and JPY/USD.) They both follow perfectly correlated geometric Brownian motions with parameters (1, 1) and (2, 2). Does the cross-exchange rate X/Z (for example EUR/JPY) also follows a geometric Brownian motion?

(a) Yes (b) No

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