PDQ stock price:102 Riskless interest rate (simple interest, i., the Annual Percentage Rate):00% Option maturity:3 months Volatility:30 Options are...

PDQ stock price:           102

Riskless interest rate (simple interest, i.e., the Annual Percentage Rate):  8.00% Option maturity: 3 months

Volatility: 0.30

Options are all European.

An option is for 1 share. Fractional shares and fractional options can be traded if you want to.

Options:           Strike   Call price  Call delta  Call Gamma         Put price Put delta Put gamma

95          11                 .75            0.0208              2 1/2            -.25         0.0208

100           8                  .63            0.0247                4                -.37        0.0247

105           6                  .50            0.0261                8                -.50         0.0261

18. Suppose you wanted to use the Black-Scholes model to create the 100 strike call synthetically. That is, you want to hold the option replicating portfolio. (Assume the current market price of 8 is the true Black-Scholes value.) For each call, you want to replicate

a)  What position should you take in PDQ stock?

b)  How much should you borrow or lend at the riskless interest rate?

c)  If you hold this replicating portfolio and tomorrow the stock price falls 4 points, will you need to buy stock, sell stock, or keep the same position to remain delta neutral?

d)  If the stock turns out to be more volatile than you expected, are you happy, unhappy, or indifferent?

(HINT: A good way to think about this is the following. Imagine you were short a 100 strike call and

you wanted to turn it into a delta neutral hedged position, that also had riskless borrowing or lending so that the total cost was zero. Now take away the short call and you are left with the stock and bond position that replicates a long position in that call.)