Deliverables consist of a pdf or doc file containing your answers and an excel file containing your data and calculations. Note that the Excel spreadsheets serve only as a support to your analysis and will be used to check your calculations and numbers provided in the analysis. All explanations have to be detailed in the pdf/doc file.

Exercise 3 : Pricing options

Pick up a stock that serves as an underlying for exchange traded option contracts. On the day of your choice, extract daily adjusted closing prices for the last year as well as the prevailing quotes for the at the money series with time to expiration closest to one month. To price the option with your model, you will need estimates of

· ·

·

Risk-free rate (use a relevant 1-month proxy such as Libor, Libor Euro, T-bill, ...) historical volatility (use annualized standard deviation of past returns using 1 year

of data)

dividends (assume no dividend will be paid until expiration)

Questions

1. Build a 4-step tree for the stock price until expiration using a conventional

Cox-Ross-Rubinstein calibration

2. Price the closest to the money call option in the tree assuming its style is European

3. PricethecorrespondingEuropeanputoption

4.It is very likely that you have found prices that defer (possibly very significantly) from market values. Explain the reason(s) that could explain why it is so.

5.Assuming your tree is an accurate representation of the world, how could you arbitrage away the differential between market prices and your estimates? Be extremely specific on which strategy you would follow and the amount of arbitrage profit you would obtain in the different states of the world. explain