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Write a small essay to analyze whether Geometric Brownian Motion is a good model for the stock price you choose, and to analyze the implications in the previous page (the picture named 28.37) one by one (pay attention to one by one), and see if they are proper descriiptions of price behaviors. Give reasons rather than just say yes or no.
Properties of St under Geometric Brownian Motion assumption
► ln(St) is normally distributed. • The log return ln(St+s) — ln(St) is normally distributed.
► ln(St) has stationary increments. • The distribution of log return ln(St+s) — ln(St) does not depend on t.
► ln(St) has independent increments. • For any ti < t2 < t3, the log returns ln(St2) — ln(St1) and ln(St3-In(St2) are independent.
► Stock price St (and ln(St)) is continuous.
► Stock price St (and ln(St)) is nowhere differentiable.
Board problem
► Choose a specific stock or stock index, and search online for its price movement over the past year. (Yahoo Finance)
► Write a small essay (300 words maximum) to analyze whether Geometric Brownian Motion is a good model for the stock price.
► Analyze the implications in the previous page one-by-one, and see if they are proper descriptions of price behaviors. Give reasons rather than just say yes or no.
► Try to be short, precise, and straight to the point.
