Exercise 14 3 1 Assume that dX X dt dW (1) Prove that ln X follows d(ln X) (2 2) dt dW (2) Derive the probability distribution of ln(X(t) X(0)) ...

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Exercise 14.3.1 Assume that dX/X= dt + dW. (1) Prove that ln X follows d(ln X) =

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Exercise 14.3.1 Assume that dX/X= μdt +σ dW. (1) Prove that ln X follows d(ln X) = (μ−σ2/2) dt +σ dW. (2) Derive the probability distribution of ln(X(t)/

X(0)).

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