here μ, a>0 and (et) is a time series of independent and identically distributed tandard Gaussian random variables. Note that Jai

Essentials Of Investments
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Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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Question 3
The Black-Scholes model is a time series (X₂) that follows the dynamics
X₁ = X₁-1*exp(μ+0€)
where μ, >0 and () is a time series of independent and identically distributed
standard Gaussian random variables. Note that
E(exp(μ+σt)) = "¹+0²
(i) Show that the log-returns of this process X, form a white noise process
(ii) Suppose E(X) = 0. Compute E(X₂).
Determine if the variance of X, is falling, remains constant or is growing in t.
Transcribed Image Text:Question 3 The Black-Scholes model is a time series (X₂) that follows the dynamics X₁ = X₁-1*exp(μ+0€) where μ, >0 and () is a time series of independent and identically distributed standard Gaussian random variables. Note that E(exp(μ+σt)) = "¹+0² (i) Show that the log-returns of this process X, form a white noise process (ii) Suppose E(X) = 0. Compute E(X₂). Determine if the variance of X, is falling, remains constant or is growing in t.
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