You own 100 shares of Amazon stock (AMZN) and are concerned that the price will go down. You do not want to sell because you have unrecognized capital gains and are in a high tax bracket.
Using the Black-Scholes model with ?std dev = .21, r=.01, t=December 2014 option, K= today's price, and ignoring dividends, answer the following:
(a) On an ongoing basis, what portfolio should you construct to offset any loss on the stock with profit from an option? (Hint: consider the delta of the stock which measures how many shares of stock equals the movements in one option. Using Black-Scholes, delta = N(d1) - 1 for a put option).
(b) What is the approximate cost per month of maintaining this hedge indefinitely? (Approximate this using 8 month option price divided by 8)
(c) If the stock price moves by $1, what is the change in value of your portfolio (stock plus option)?
(d) If the stock price moves by $100, what is the change in value of your portfolio? Why is it different than part (c)?