A stock price is currently $48. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 3% per annum with semi-annual compounding.

Part I. Use the two-steps binomial tree model to price a 6-months European put option with an exercise price of $51.

Part II. Assume you have sold the above put option to your client and charged him a fair price. Discuss how you can hedge your risk to avoid a big loss if the stock price turned out to be $1 in 6-months.