1. Gamma Hedging The Gobs of Money Machine Wilhelm's Warriors
No Hedgetation
Gamma Hedging

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3. Confidential Peer Evaluation
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4. Example diagnostic: why is the smart hedger stuck ?

5. Main parameters to tweak
Frequency of hedging (HedgingToday)
Family Delta threshold (NeedToHedge)
Type of transaction preferences (CalcCandidateRecScores)
A-E options preferences (scoring rules)
Delta threshold (CalcQtyNeededToHedge)
Family delta target (CalcQtyNeededToHedge)
Max buy cushion (MaxPurchasePossible)
Available cash cushion (AvailableCashIsLow)
Max margin cushion (TooCloseToMaxMargins)
Max short cushion (MaxShortWithinConstraints)

6. Hedging
Gamma, Vega, Theta & Rho

7. Delta Neutral Portfolio Decay
Payoff
Put portfolio
Call portfolio
Stock price
Source: Delta Gamma Hedging and the Black-Scholes Partial Differential Equation - S. Raju, JEFE 2012

8. Delta & Gamma neutral Portfolios
Payoff
Call portfolio
Put portfolio
Stock price
Source: Delta Gamma Hedging and the Black-Scholes Partial Differential Equation - S. Raju, JEFE 2012

9. Gamma
Family Delta (D) measures the change in portfolio value as the underlier’s price S changes (~speed).
Family Gamma (G) measures the rate of change in portfolio value as S changes (~acceleration).

10. Meaning of Gamma
If Gamma is small (abs.), small changes in S will not affect much Delta (and your portfolio value) , so there is less need to take immediate rebalancing action.
If Gamma is large, small changes in S will affect Delta (and your portfolio value) significantly, so there is a stronger need to take immediate rebalancing action.

11. How to Calculate Gamma Gamma = N’(d1) SsÖ t N’(d1) = e –(d1)2/2
Ö (2 p)
d1 as in Black Scholes
Gamma
N’ is the prob density function for a standard normal distribution.
Stock price S
Strike

12. Gamma of a Portfolio of Related Securities
Gfamily = S qtyi * gi

13. Gamma-Neutral Portfolio
More stable than a delta neutral-only.
Cannot use the stock to reach Gamma neutrality because the stock has Gamma = 0
1) Gportfolio <> 0
2) Gportfolio + gx qtyx = 0
3) qtyx = -Gportfolio / gx
Warning: Acquiring qtyx will disturb Delta neutrality. You will need to rebalance.

14. Delta Gamma Delta It’s a financial strategy, not a sorority.
Find out what you need to achieve Delta neutrality.
Find out what you need to achieve Gamma neutrality.
Find out what you need to re-achieve Delta neutrality. Stock is ideal because it will not affect Gamma.

15. Three Dark Horses Simultaneous Delta Gamma Conditional Gamma
Synthetics
Come and see me – not on the last day!

16. Simultaneous Delta Gamma
Dportfolio + dx1 qtyx1 + dx2 qtyx2 = 0
Gportfolio + gx1 qtyx1 + gx2 qtyx2 = 0
All known except qty x1 and qty x2 {

17. Conditional Delta Gamma
If below target -> delta only else Delta + Gamma

18. Offset the Position with a Synthetic Security
Profit & Loss
Perfect hedge, but costly.
Synthetic Short position
Long position to hedge
Stock price
Total Payoff

19. Put-Call Parity
For European Ps and Cs that have the same strike K, and expire by the same time t:
P + S = C + K e-rt
We can solve for S, P, or C, effectively synthesizing a security with a combination of the other two and some interest- earning cash.
Example: S = C + Ke-rt – P and
- S = - C - Ke-rt + P

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21. The RoboTrader
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22. The two timers (simplified)
Timer 1 (spy)
Timer 2 (seconds on screen)
Start
Check the date on the DB
New date?
Decrease the seconds by 1 No
Yes
Run daily routine
Set seconds to 59
Less than 0?
Yes No