Q$6.$ You wish to create a Delta$-$neutral position with two different puts but without any shares of the underlying

assets. The market premiums of these puts are: $p_1$ and $p_2.$

The value of this portfolio is: $,V=(p_1)n(p_1,s)+(p_2)n(p_2,s).$

Derive the formula for the relationship between the two calls so as to create a Delta$-$neutral position. Use the

same method that I used on slide $31CH.17$ but with only the two calls; no stock shares.

Q$7.$ A financial institution just sold $1,000$ CBOE of the $170,$ AUG puts. Use the formula you derived in Q$6$ to explain

what position will be taken in the OCT $165$ put to create a Delta$-$neutral portfolio, using no shares of the

underlying asset.

Q$8.$ Consider the following data.

Calculate the Delta, Gamma and Vega of the following portfolio:

Portfolio $=\{$short $6$ of calls $1$; short $15$ of puts $1$ ; long $15$ of calls $2$; short $20$ of calls $3\}$