Question

The following information applies to the next three questions.

Stock XYZ is currently selling for $100. The risk free rate is 4.5% and a June 100 call on stock XYZ is selling at 17.80 with a delta equaling 0.6227. You plan to sell 100 contracts of June 100 call on XYZ.  

14.   If the gamma of this June 100 call option is 0.0095. A June 105 call option on this stock XYZ is selling for $15.6929 with a delta of 0.5756 and gamma of 0.0098.   We still plan to sell 100 contracts of June 100 call, how many shares of XYZ and number of contracts of June 105 call do we need to use to be delta and gamma neutral?

          a. buy 1000 shares and 83contracts of June 105 call

          b. sell 1000shares and 83 contracts of June 105 call

          c. buy 647 shares and buy 97 contracts of June 105 call

          d. sell 647 shares and sell 97 contracts of June 105 call

15. How much is the initial investment?

1. $27,581
2. $38,921
3. $46,372
4. $51,398

Answer 1

14) for delta nuetral stretergy

Delta of june100 call of 100 contract= -(100*100*0.6227) =(-6227) deltas

So inorder to makr delta nuetral we need to add 6227 delta

So we have to buy shares as well as june 105 contracts

So choose option C

Buying 647 shares and buying 97 contracts of june 105 call

If we calculate delta for this =

647(delta of shares ) + (97*100*0.5756) = +6229 deltas

So adding both this stretergy we can make it delta neautral

15)total investment require =

= (647*$100)+(15.69*100*$100) -(17.59*100*$100)

= $46,372