1. (4 points) Consider a non-dividend paying stock. The current price of the stock is $50. In a 6-month period, the stock price either goes up by 20% or down by 20%. The risk free interest rate is 1% per year with continuous compounding. Consider a 1-year at-the-money European put option. Compute the risk neutral probability of the stock price going up. What's the value of the option? If you sell 100 put options, how do you delta hedge initially? How do you adjust your hedge if stock price goes down in 6 months