1.(10pt) European call and put on a stock both have a strike price 80 and an expiration date of 3 months. Both trade

for 12$. The risk free rate is 10% per year, the current stock price is 76$ and a 4$ dividend is expected in 1 month.

Is it possible to create an arbitrage using call, put, stock and cash. If yes, explain how to do the arbitrage.

2.(5pt) Explain why an American option on a stock paying continuous dividend yield is always worth as much as its

intrinsic value. Give a numerical example of a situation when European option is worth less than intrinsic value.

(Give the numerical value of stock price, strike price, time to expiration, etc.)

3.(5pt) Explain the European call-put parity argument. Why it can not be used for American options.

9.(5pt) Suppose that the value X of a variable that follows a Standard Brownian Motion is initially 30. The time is

measured in years. Write the probability density function of the distribution of X after 0.5 year, 1 year, 2 years,

4years?

10.(10pt) Suppose the stock price is 30, the riskless rate is 2%. What is the price of a 1 year call struck at 30 if the

volatility is 0. How would you hedge the call.