Question

An options dealer has a short position of 6,000 in DELCO call options. The call options have a delta of 0.60, a gamma of 0.04 and vega of 6. (please show workings)

116. The option dealer’s portfolio has a: (a) delta of -3,600 and a gamma of -240 (b) delta of 3,600 and a gamma of -240 (c) delta of -2,400 and a gamma of 240 (d) gamma of 240 and a vega of 1,000.

117. The dealer can make his option portfolio delta-neutral by: (a) buying 2,400 DELCO stock (b) selling 1,000 DELCO stock (c) buying 3,600 DELCO stock (d) buying 600 DELCO stock.

118. Assume that a DELCO put option with a delta of -0.50 and a gamma of 0.05 is available. The dealer can make his initial portfolio both delta-neutral and gamma-neutral by: (a) buying 3,600 DELCO stock (b) buying 3,360 DELCO stock and selling 480 DELCO puts (c) selling 3,600 DELCO stock and buying 480 DELCO puts (d) buying 6,000 DELCO stock and 4,800 DELCO puts.

Answer 1

Option Having  

delta = 0.60

gamma = 0.04

vega = 6

Total Position = short position of 6,000 = - 6000 ( -Ve due to Short Position)

So,

Portfolio Delta = Total Position * delta =  - 6000 *  0.60 = - 3600

Portfolio gamma = Total Position * gamma = - 6000 * 0.04 = -240

Portfolio vega = Total Position * vega =   - 6000 * 6 = -36,000

116 . Ans : Options Portfolio = (a) delta of -3,600 and a gamma of -240  

Portfolio Delta is = - 3600

To Make the Portfolio Delta Neutral Dealer can buy 3600 DELCO stock. ( Delta of a stock is = +1 )

117. Ans: Portfolio Delta Neutral   (c) buying 3,600 DELCO stock

a put option with a delta of -0.50 and a gamma of 0.05

Now no of Put options require to make the portfolio gamma neutral =  Portfolio gamma / Put Option Gamma  

= 240 / 0.05 = 4800

But this 4800 No of Put Option will affect Delta of the Portfolio

Portfolio Current Delta = Portfolio Previous Delta +  no of Put options * Put Delta

= -3600 + 4800 * ( -0.5) = -6000

So Portfolio Delta becomes = -6000

To make it Delta Neutra we need 6000  DELCO stock

118. Ans : Total 6000 DELCO stock & 4800 No of Put Option require to make the portfolio delta-neutral and gamma-neutral . ( Option D)