Delta-gamma neutral options

F

faust

Questions:

1. A delta-neutral option portfolio has a position gamma of +300. If call options have a (percentage) delta of 0.58 and gamma of 0.120, what trades will neutralize the delta and gamma of the portfolio?
a. Long 1,500 put options and sell 950 shares
b. Short 1,500 put options and buy 950 shares
c. Long 2,500 call options and sell 1,450 shares
d. Short 2,500 call options and buy 1,450 shares

2. A market maker writes (sells) a contract of 100 call options, where the percentage (per option) delta of the call options is 0.60 and the gamma is 0.080. The market maker wants to neutralize both the delta and gamma of this position (delta-gamma-neutral) with two additional trades: the underlying shares; and put options on the stock with percentage delta of -0.40 and gamma of 0.020. What are the trades?
a. Buy 200 put options and buy 80 shares
b. Sell 200 put options and sell 80 shares
c. Buy 400 put options and buy 220 shares
d. Sell 400 put options and sell 220 shares

3. A delta-neutral option portfolio has a large and positive position theta. Which of the following trades is most likely to neutralize the portfolio's gamma?
a. Buy call options
b. Write put options
c. Sell shares
d. None of the above: theta must be negative!

4. A delta-neutral portfolio of options is net short and the options are, on average, at-the-money (ATM) with near-term maturities. Which of the following is most likely true about the portfolio's theta?
a. Large and negative
b. Small and negative
c. Small and positive
d. Large and positive
 
I like these types of questions - as a lot has to do with terminology that differs depending on where you worked, when/how you learnt options....
so while I sit and wait - answers with rationale.

faust said:
Questions:

1. A delta-neutral option portfolio has a position gamma of +300. If call options have a (percentage) delta of 0.58 and gamma of 0.120, what trades will neutralize the delta and gamma of the portfolio?
a. Long 1,500 put options and sell 950 shares
b. Short 1,500 put options and buy 950 shares
c. Long 2,500 call options and sell 1,450 shares
d. Short 2,500 call options and buy 1,450 shares
More...

Currently: Long Gamma - hence to neutralise long gamma you need to sell gamma. Either b) or d)
If you choose b) you are effectively going long delta and going long shares.....unlikely as the portfolio is already delta neutral,
answer:
if you choose d) gamma of .12*2500 call options =300 Gamma neutralised, and the 1450 shares hedge the calls.

faust said:
2. A market maker writes (sells) a contract of 100 call options, where the percentage (per option) delta of the call options is 0.60 and the gamma is 0.080. The market maker wants to neutralize both the delta and gamma of this position (delta-gamma-neutral) with two additional trades: the underlying shares; and put options on the stock with percentage delta of -0.40 and gamma of 0.020. What are the trades?
a. Buy 200 put options and buy 80 shares
b. Sell 200 put options and sell 80 shares
c. Buy 400 put options and buy 220 shares
d. Sell 400 put options and sell 220 shares
More...

Currently: - trader is short 60 deltas, and short 8 gamma.
To hedge he needs to buy deltas and buy gamma.
So - b) and d) are selling gamma - these are out, leaving a) and c)
a) would be delta neutral, (200*.4=80shares) hence the original trade would still be naked short....not the answer
answer:
c) buys puts and hedges them (400*.4=160), and also hedges the short calls (60+160=220)




faust said:
3. A delta-neutral option portfolio has a large and positive position theta. Which of the following trades is most likely to neutralize the portfolio's gamma?
a. Buy call options
b. Write put options
c. Sell shares
d. None of the above: theta must be negative!
More...

Here is an issue of terminology. I always learnt - long options had negative theta, short options had positive theta ---- this was how it was represented in our PL. However, all options decay and hence theta as such is always negative.
So d) could certainly be the answer.

........looking at the other answers, assuming you could have positive theta, meaning you are short options......
To neutralize the gamma you need to buy options. Only a) is a viable answer. (though by itself covers the gamma, its leaves a delta position)

If you think its a trick question I would go for d), otherwise I would go for a) (my choice)

faust said:
4. A delta-neutral portfolio of options is net short and the options are, on average, at-the-money (ATM) with near-term maturities. Which of the following is most likely true about the portfolio's theta?
a. Large and negative
b. Small and negative
c. Small and positive
d. Large and positive
More...

Currently: ATM short options near expiry (Theta is large as decay is at a rapid decline).
Leaves a) and d)
Again a lot depends on your terminology, but as I think theta can be both positive and negative, and you are net short in the portfolio (meaning positive time decay PL - you are receiving money)
answer d)

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thanks for the memory exercise, and helping me avoid the last 15mins of chop.
 
I always figure you want people trading options who never bothered to work out how they work......by not doing their homework.
;)
 
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