Build a Derman and Kani- type (binomial) implied arbitrage-free volatility tree. The number of periods will be Öve. You may use options on
any asset class, as long as they are liquid (options on stock market indices such as S&P 500 are quite suitable) for any period from 2010 onwards. Make sure that you take care of dividends ( if applicable), early optionality (eg., American options, if applicable). Provide details of the interpolation/extrapolation methods to con-struct the input option/implied volatility data. Make explicit assumptions about centering the tree and construct also the implicit Arrow-Debreu tree.
Discuss how you handle “bad probabilities”, i.e., violations of the no-arbitrage condition.
As a baseline, you should construct a similar constant volatility binomial tree (for example, Cox-Ross-Rubinstein). Calculate the “Greeks” and compare them with your Öndings from the implied volatility tree. Discuss your Öndings.