Greeks: IBM stock is currently priced at $50. IBM pays no dividend within the next 6...

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Greeks: IBM stock is currently priced at $50. IBM pays no dividend within the next 6 months. Consider a European call and a European put, both struck at $50, on IBM stock, both with maturity 7 = 3 months. IBM stock has a volatility of 25%. The continuously-compounded interest rate is 6% per annum. (a) Assume that IBM stock price is described by the lognormal model (i.e., Black-Scholes holds). Calculate the replicating portfolio, com- posed of IBM stocks and borrowing/lending, for both the call and the put. Note: You should only need B-S to calculate one of them; the other can can be obtained using P-C parity. What are the prices of these portfolios? (b) If you're long one of the above calls, how many shares of IBM stocks and how many of the above puts do you need to buy in order to create a Delta- and Gamma-neutral portfolio? Note: Once you get into this you should be surprised by how easy it is if what you're doing is complicated, then it's probably wrong! (c) Suppose you currently own a portfolio of options on IBM stock. Your portfolio has the following Greeks: A r 50,000 -5, 000/$ -$500, 000/year -$300,000 $400,000. After holding your portfolio for a week, IBM stock is trading at $51 and the interest rate has fallen to 5.85%. IBM stock volatility is still 25%. What is the change, approximately, in market value of your portfolio? Greeks: IBM stock is currently priced at $50. IBM pays no dividend within the next 6 months. Consider a European call and a European put, both struck at $50, on IBM stock, both with maturity 7 = 3 months. IBM stock has a volatility of 25%. The continuously-compounded interest rate is 6% per annum. (a) Assume that IBM stock price is described by the lognormal model (i.e., Black-Scholes holds). Calculate the replicating portfolio, com- posed of IBM stocks and borrowing/lending, for both the call and the put. Note: You should only need B-S to calculate one of them; the other can can be obtained using P-C parity. What are the prices of these portfolios? (b) If you're long one of the above calls, how many shares of IBM stocks and how many of the above puts do you need to buy in order to create a Delta- and Gamma-neutral portfolio? Note: Once you get into this you should be surprised by how easy it is if what you're doing is complicated, then it's probably wrong! (c) Suppose you currently own a portfolio of options on IBM stock. Your portfolio has the following Greeks: A r 50,000 -5, 000/$ -$500, 000/year -$300,000 $400,000. After holding your portfolio for a week, IBM stock is trading at $51 and the interest rate has fallen to 5.85%. IBM stock volatility is still 25%. What is the change, approximately, in market value of your portfolio?

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a Using BlackScholes Call price 296 Put price 296 from putcall parit... View the full answer