For the stock that corresponds to your Group, select an option expiry date among the available ones in the market so that >0.5 years. Given the spot price of the stock (0), select three strike prices 1,2 and 3 near the money such that 1<2<36.

1. a) Pricing Call and Put options with strike price 2 and maturity (in detail calculations).

The time horizon should be divided into 5 intervals of duration each. Consider that the stock price may increase by and decrease by on each time interval. The volatility of the stock price is the historical volatility found in Question 2, part (c).

- Calculate analytically the probability

- Draw the binomial tree for the stock price evolution

- Provide and explain the formula of calculating the probabilities of reaching each node

- Price the European Call and Put Options (show the required trees; explain)

- Price the American Call and Put Options (show the required trees; explain)

- Comment on the difference of the premiums

1. b) Pricing Call and Put options with strike prices 1,2 and 3 and maturity .

The time horizon should be divided into 15 intervals now of duration each. Consider that the stock price may increase by and decrease by on each time interval. The volatility of the stock price is again the historical volatility found in Question 2, part (c).

- Calculate analytically the probability

- Price the European Call and Put Options of strike price 17.

- Price the European Call and Put Options of strike price 2.

- Price the European Call and Put Options of strike price 3.

- Compare the European Call and Put premiums for strike price 2 of (a) and (b)

- Explain the difference between the calculated premiums and those in the market.

1. c) Given the premiums and (=1,2,3) that correspond to the options with strike prices 1,2 and 3 that have been already calculated, built the following trading strategies and discuss their suitability:
2. - Option (2) and underlying asset. i) Covered Call and ii) Protective Put
3. - Multiple options (1,3) of the same type. i) Bull Spread with Calls and ii) Bear Spread with Puts
4. - Combinations. i) Strip (2) and Butterfly Spread (1,2,3)