For all problems in this section, use the binomial tree model. Unless otherwise stated, assume no arbitrage.

A stock is currently priced at $32.00. The risk free rate is 8.5% per annum with continuous compounding. In 17 months, its price will be either $36.16 or $27.52.

(a) If your portfolio is long a 17 month European put with strike $30.65, how many stocks should you acquire to make your portfolio risk-free over the next 17 months?

(b) If your portfolio is short a bond which pays $43.00 in 17 months as well as short 12 17-month European calls, each with strike $30.65, how many stocks should you acquire to make your portfolio risk-free in 17 months?