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

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

Essentials of Business Analytics (MindTap Course List)
Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN:9781305627734
Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Chapter8: Time Series Analysis And_forecasting
Section: Chapter Questions
Problem 18P: Consider the following time series: Construct a time series plot. What type of pattern exists in...
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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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