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Evaluate the option premiums, call and put, European and American, based on a binomial lattice framework. Compare your results with the given European option price, examine the effectiveness of your selected method, and make improvements where necessary.

1. Use the daily market data to statistically evaluate the historical volatility for the share price. Collect information on the company’s annual dividend paid
and assess its dividend yield. For your chosen origination date, collect data on the annual interest rate for various expiration dates.

2. Evaluate the option premiums, call and put, European and American, based on a binomial lattice framework. Compare your results with the given
European option price, examine the effectiveness of your selected method, and make improvements where necessary.

3. Report the Greeks and perform any sensitivity analysis.

4. Derive the American put exercise boundary.

5. Extend your analysis to more complex exotic options.