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(a) Suppose that observations on a stock price (in dollars) at the end of each of 6 consecutive weeks are as follows: 20.0; 21.2; 23.6;

(a) Suppose that observations on a stock price (in dollars) at the end of each of 6 consecutive weeks are as follows:

20.0; 21.2; 23.6; 21.9; 20.5; 21.7

Estimate the annualized volatility of logarithmic returns that is used in the Black Scholes formula. Show your calculations.

(b) The plot of the implied volatility for one-year options against the stock price was flat, but now has taken the shape of a smile. That is, it is U shaped. Provide some reasons for the change in shape.Be very clear and precise.

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