# solution

.FIN672: Financial Instruments and Derivatives

. Answer all of the provided questions in a Word document, being sure to explain your answer, and show your work if required.

• (An investor for a firm buys a call on ABC stock with a strike price of K and writes a put with the same strike price and maturity. Assuming the options are European and that there are no dividends expected during the life of the underlying, how much should such a portfolio cost?
• A stock is currently trading at 80. Your firm holds a portfolio consisting of the following:
• (a) Long 100 units of stock.

(b) Short 100 calls, each with a strike of 90.

(c) Long 100 puts, each with a strike of 70.

Suppose the delta of the 90-strike call is 0.45 while the delta of the 70-strike put is -0.60. What is the aggregate delta of this portfolio? We consider each component of the portfolio individually, and then add them up.

• A stock is currently trading at 80. There are one-month calls and puts on the stock with strike prices of 70, 75, 80, 85, and 90. The price and delta of each of these options is given below:
• Strike: 70 / 75 / 80 / 85 / 90

Call Price: 10.60 / 6.47 / 3.39 / 1.50 / 0.56

Put Price: 0.30 / 1.15 / 3.05 / 6.14 / 10.18

Call Delta 0.92 / 0.77 / 0.54 / 0.31 / 0.14

Put Delta: -0.08 / -0.23 / -0.46/ -0.69 / -0.86

For each of the following portfolios:

(a) Long 100 units of stock, short 100 units of the 80-strike call.

• Find the current value of the portfolio
• Find the approximate value of the portfolio following a \$1 decrease in the stock price.
• (b) Long 1000 units of the 80-strike call and 1174 units of the 80-strike put.

• Find the current value of the portfolio
• Find the approximate value of the portfolio following a \$1 decrease in the stock price.

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