Exam perspective - Delta Neutralising Positions

bhar

Active Member
Hi
Current Position - Long Call; Position Delta +ve; Delta Neutralising trx - short stock
Current Position - Short Call; Position delta -ve; Delta Neutralising trx - Long stock
Current Position - Long Put; Position Delta -ve; Delta Neutralising trx - Long stock
Current Position - Short Put; Position delta +ve; Delta Neutralising trx - short stock

Please correct me, if any mistakes.
 

David Harper CFA FRM

David Harper CFA FRM
Subscriber
Hi bhar, yes agreed. Neutralizing can be achieved various ways, including with options, but as stock has %delta = 1, long stock has position delta = +quantity*1 and short stock has position delta = -quantity*1, so will neutralize as you say

similar is here @ http://forum.bionicturtle.com/threads/p1-t4-204-option-greeks.6223/#post-20016

  • long 100 calls = position delta of +100 * +0.60 = +60; i.e., always positive position delta
  • short 100 calls = position delta of -100 * +0.60 = -60; always negative position delta
  • long 100 puts = position delta of +100 * -0.40 = -40; always negative position delta
  • short 100 puts = position delta of -100 * -0.40 = +40; always positive position delta
    generically: position Greek = +/- Quantity * percentage Greek
And further detail here @ https://forum.bionicturtle.com/threads/l1-t4-7-dynamic-delta-hedging.4839/
i.e.,
"David's ProTip: I learned from Carol Alexander a useful semantic distinction (not in Hull). Consider a position in 100 call options with per-option delta of 0.6:
  • The Percentage Delta is 0.6; this is the unitless first partial derivative, dc/dS
  • The Position Delta is 60 because Position Delta = Quantity * Percentage Delta.
  • If we are long, we use (+) quantity: Position Delta (long 100 calls) = +100 * 0.6 = +60;
  • If we are short , we use (-) quantity: Position Delta (short 100 calls) = -100 * 0.6 = -60
  • To neutralize is to get the position Greek to zero
This is robust, for example:

Selling puts increases position delta because -QTY * -% delta = +position delta; i.e., % delta of puts always negative; % delta of calls is always positive
Selling calls or puts decreases position gamma because -QTY * +% gamma = - position gamma; i.e., % gamma is always positive for both calls & puts

Just as we use dollar duration (not modified duration) to neutralize duration in the portfolio, we neutralize an option Greek by summing Position Greeks to zero. I often see candidates trying to neutralize with percentage delta directly, but you can't, you need to sum the "Position" Greeks. I hope that's useful! David"
 

skoh

Member
Hi David,

So for question 7.4. in L1.T4. Valuation & Risk Models, Option Greeks,

The answer should be A instead? (long 6 shares)

Rgds
 
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