1. A stock price is currently $40. Over each of the next two three-month periods, it is expected to go up by 10% and down by 10%. The risk free interest rate is 12% per annum with continuous compounding.
   1. What is the value of a six-month European call option with a strike price of $42?
   2. What is the value of a six-month European put option with a strike price of $42?
   3. Verify the put call parity.
   4. What is the value of a six-month American call option with a strike price of $42?
   5. What is the value of a six-month American put option with a strike price of $42?
   6. For the American put, what is the hedge ratio today?
   7. If you have 100 shares of the underlying stock, how do you use American put to hedge your position?
   8. At the end of the first year, if the stock goes up, what is your hedge ratio using the American put? How do you rebalance your portfolio to hedge your position?
   9. At the end of the first year, if the stock goes down, what is your hedge ratio with the American put? How do you rebalance your portfolio to hedge your position?

This is on binomial model and hedge ratio