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(a)State the definition of a Geometric Brownian Motion (GBM) St , and its analytic solution, given the initial value S0.Derive the distribution of loge(ST ),

(a)State the definition of a Geometric Brownian Motion (GBM) St , and its analytic solution, given the initial value S0.Derive the distribution of loge(ST ), and hence of ST .

(b) State the general form of ARCH(q), the autoregressive conditional heteroscedasticity model of order q.

Explain why the model gained its popularity.

Discuss one way how the ARCH model can be extended.

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