The Black\ -\ Scholes ABC.\ \ According to the Black\ -\ Scholes model, what should be the price of a put option on an\ asset with current value S \ =\ \ 41\ ,\ annual volatility a \ =\ \ 0.23\ ,\ one\ -\ year maturity, and a strike of\ K \ =\ \ 43.\ Assume the annual risk\ -\ free rate is \ 7\ %\ .\ \ For the option in the previous question, what is the replicating portfolio? You do not need to specify the full dynamic trading strategy, just the shares of the underlying asset and the amount of cash you would need to hold one year prior to maturity with the asset price\ being at \ 41.\ Shares\ =\ ,\ Cash\ =\ \ How would the replicating portfolio change if the underlying asset went down to \ 39\ ?\ Shares\ =\ ,\ Cash\ =\ 170