Your own portfolio currently consists of 100 shares of Lilac Inc stock and it has a current market price of $105 per share. You consider writing a single European call option contract on Lilac stock. (Recall that a single option contract consists of options on 100 shares of the stock.) You plan to use cash proceeds from the option contract sale to immediately purchase additional shares of Lilac stock at the current market price. You have decided to write the option contract with a $125 strike price and a 3 months maturity. The annualized volatility (standard deviation) of the stock has historically been approximately 50%, and the current annualized risk-free rate is 3%.
a. How much money do you expect to receive from the sale of the option contract according to the Black-Scholes model? How many additional shares of Lilac will you be able to purchase given this price? (Note: assume you can buy partial shares)
b. If you write the option contract at the price you calculated in part (a) and buy the additional shares, what will be the total value of your portfolio in 3 months (on the expiration date of the option) for each of the following possible stock prices: $80, $100, $120, $140, $160? (include payoff)
c. Calculate the break-even expiration date stock price at which your total portfolio value will be the same if you undertake this strategy versus if you just hold onto your existing shares and do not write the option contract or buy any additional shares. (I.e., the price at which you will be indifferent on the expiration date between undertaking the strategy and not undertaking it).
d. You could alternatively consider writing a put option contract to raise cash rather than writing a call option contract. Given your answers above, how much cash would you expect to receive if you wrote a single put option contract (on 100 shares) with the same strike price and expiration date as the call option contract described above?