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.

The assignment task is to numerically evaluate the call and put option prices, both
European and American, on an underlying stock index asset by using the lattice
framework.
The selected company and the origination date for evaluating the option value must
be registered1. Although it is acceptable that more than one student may select the
same company, the origination dates must be different.
You are required to complete the following:
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.