Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). You want to protect your long position against losses and decide to buy a European put option on AAPL with a strike price of $180.15 and an expiration date of 1-year from today. The continuously compounded risk free interest rate is 8% and the stock pays no dividends. The current stock price for AAPL is $200 and its volatility is 30%. Assume all options premiums are exactly equal to the Black-Scholes options prices. Once you discover how expensive the put option premium is, you decide to sell a 1-year call European call option on AAPL to help pay for the put option. You are free to choose the strike price of the call option. At what strike price will the call option you sell pay for the put option you buy? $280.15 O $270.15 $180.15 $200 Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). The continuously compounded risk free interest rate is 8% and the stock pays no dividends. You also are given: The current stock price for AAPL is $200 The volatility for AAPL is 30% The continuously compounded expected growth rate for AAPL is j = 4.5% You want to protect your long position against losses and decide to hedge your long position with the following options trades: Buy a European put option on AAPL with an expiration date of 1-year from today with strike price of $200 Sell a European call option on AAPL with an expiration date of 1-year from today with strike price greater than $220 The strike price of the call option is chosen carefully so that the net option premium including both options is zero. The hedged portfolio contains long 1 share of AAPL stock, long 1 put option, and short one call option. Assume all options premiums are exactly equal to the Black-Scholes options prices. What is the probability that this hedged portfolio value will be strictly greater than than the price of AAPL in one year? O 100% O 50% 0 0% 0 15.4%