For more information and regulations about the capstone assignment, please refer to EleUM>My SBE - Before and after graduation - Capstone assignment

Implied Binomial Trees: The option pricing framework put forward by Black and Scholes (1973) and Merton (1973) provides the fundamental building block for option pricing in practise. The main inside of this approach is that one can price options by dynamically adjusting a replicating portfolio consisting of the underlying asset and a risk free investment. Although that inside is still valid, there have been uncovered empirical shortcom- ings of the original model put forward by Black-Scholes-Merton. In reaction to these empirical observations researchers have put forward more general models to better fit these observations.

During this capstone assignment the student is expected to cover at least the fol- lowing questions
1. How does the binomial model of Cox, Ross, and Rubinstein (1979) relate to the Black-Scholes-Merton model?
2. Using the papers by Rubinstein (1994), Derman and Kani (1994) and Bakshi, Cao, and Chen (2000) what are the empirical observations not captured by the Black-Scholes-Merton model?
3. Although Rubinstein (1994), Derman and Kani (1994) and Bakshi, Cao, and Chen (2000) use different model approaches, what part do the solutions in both papers have in common?
4. What is the main difference between the binomial tree proposed in Cox, Ross, and Rubinstein (1979) and Derman and Kani (1994)?
5. How is the binomial tree in Derman and Kani (1994) setup, i.e., calibrated? (HINT: Use Section 16.6 in Sundaram and Das (2011))

In addition to the literature listed below, make sure that you review at least 5 additional articles of your own choice.

- Bakshi, Gurdip, Charles Cao, and Zhiwu Chen, 2000, Do Call Prices and the Un- derlying Stock Move in Opposite Directions?, Review of Financial Studies 13, 549–584.

- Black, F., and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, 637–654.

- Cox, J.C., S.A. Ross, and M. Rubinstein, 1979, Option pricing: A Simplified Ap- proach, Journal of Financial Economics 7, 229–263.

- Derman, E., and I. Kani, 1994, The Volatility Smile and Its Implied Tree, Working paper, Goldman Sachs Quantitative Strategies.

- Merton, R.C., 1973, Theory of Rational Option Pricing, Bell Journal of Economics and Management Science 4, 141–183.

- Rubinstein, M., 1994, Implied Binomial Trees, Journal of Finance 49, 771–818.

- Sundaram, R. K., and S. R. Das, 2011, Derivatives: Principles and Practice. (McGraw-Hill).