a. Tommygun's current stock price is $80, and the stock does not pay dividends. The instantaneous risk-free rate of return is 7%. The instantaneous standard deviation of Tommygun's stock is 40%. You want to purchase a put option on this stock with an exercise price of $71 and an expiration date 45 days from now.

Using Black-Scholes, the put option should be worth ______ today.

b.

You would like to hold a protective put position on the stock of Ximera Corp to lock in a guaranteed minimum value of $50 at year-end. Ximera currently sells for $50. Over the next year, Ximera's stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Ximera Corp. Suppose the desired put options with X = 50 were traded. What would be the hedge ratio for the option?