Exam perspective - Delta Neutralising Positions

[bhar]

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]

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"

 

[bhar]

Ok great. The additional thread has clarified some more doubts. Thanks David.

 

[skoh]

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