i******w
发帖数: 407 | 1 t = 0: 1 USD = 1 EUR
t =T: two possible outcomes, 1.25 USD = 1 EUR or 0.8 USD = 1 EUR, each with
0.5 probability. so expectation is 1.025 USD = 1 EUR. But we can use the
same argument as following: at T, 1 USD = 0.8 EUR or 1 USD = 1.25 EUR, so 1
USD = 1.025 EUR. Combine these two, we get 1 EUR = 1.025 USD = 1.025^2 EUR,
this is weird, so what's wrong here? | k*****y
发帖数: 744 | 2 E(1/X) != 1 / E(X) in general | k*****n
发帖数: 117 | 3 nothing wrong with the analysis
E[EUR/USD] = 1.025
E[USD/EUR] = 1.025
However to say
1 EUR = 1.025 USD = 1.025^2 EUR is wrong.
because E[EUR/USD * USD/EUR] <> E[EUR/USD] * E[USD/EUR] |
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