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

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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. Optional mini-projects
auto dividend cashing (scheduled transactions)
gamma hedger
differential thresholds for hedging
differential family deltas
intentional crashes
edit portfolio on the fly
bang for the buck (synch/auto)
auto/synch training
july options
delta for dividend-paying securities
"extra profits" button
error viewer

7. Hedging
Gamma, Vega, Theta & Rho

8. 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

9. 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

10. 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).

11. 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.

12. 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

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

14. 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.

15. 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.

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

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

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

20. 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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22. The RoboTrader
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