Apple stock is currently trading at $170. Assume that Apple stock can go up by 15% (U = 1.15) or down by 8% (D = 0.92) in each period (3-month). The risk free rate is 4% annual (r = 1 + 4%/4). The exercise price of call and put options considered on Apple stock is $165.

Estimate the following:

a. Develop a 4-period stock price, call and put pay-offs in the possible states (Binomial)

b. Compute Apple 4-period Call Option Price today (Binomial)

c. Compute Apple 4-period Put Option Price today (Binomial)

d. Show that the Put-Call Parity works

e. This Apple call option is now trading at $17 with an implied volatility of 40%. If the historical observed volatility of Apple is 26%, provide a trading recommendation for this Apple Call Option with your rationale.