Gamma Hedging The Ira Harris Experience Wilhelm's Warriors No Hedgetation The Gobs of Money Machine Gamma Hedging

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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)

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Hedging Gamma, Vega, Theta & Rho

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

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

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.

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

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

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

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.

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.

Two More Dark Horses Simultaneous Delta Gamma Conditional Gamma Come and see me – not on the last day!

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