Q$1.$ Given the following data, calculate the Delta, $(),$ Gamma, $(,$ and Vega, $($v$),$

of portfolio $1,$ described in the left column of the table.

Q$2.$ Using the same data given in Q$1.$ determine the number of shares of the

underlying stock that must be

held together with portfolio $1$ in order to create a

new position that is:

Delta $-$ neutral

Q$3.$ Using the same data given in Q$1.$ calculate the number of shares in calls $5$ that will

be required to create a Delta$-$neutral position with Portfolio $1.$ No shares of the underlying

stock are used in this problem.

Q$4.$ Using the same data given in Q$1.$ determine the number of shares of the underlying

stock and the number of shares in Call $5$ that must be held together with portfolio $1$ in

order to create a new portfolio that is:

Delta $-$ Gamma neutral

Q$5.$

$5\mathrm{.}1$ A market maker just shorted $1,000$ calls of call $5$ from the table above. The market

maker wishes to begin a Dynamic$-$Delta strategy. How many shares of the underlying stock

should the market maker hold?

$5\mathrm{.}2$ A week later the stock price went down and the Delta of call $5$ was recalculated to

be $\mathrm{.}45.$ How will the market maker adjust his portfolio in order to delta neutralize it$?$

Q$6.$ The DJA level today is $34,200\mathrm{.}67$ points. Assume that the Divisor is $D=$

$0\mathrm{.}1111111111111.$

If the stock price per share of one of the stocks that are in the portfolio associated with the

DJIA falls by $$3\mathrm{.}75,$ calculate the new DJIA level.