Papale on the Basics: Gamma

It’s that time of year again.  Flowers or chocolates.  Pink or white or red.  Dark or milk.  Valentine’s Day is what I like to call the “Hallmark Holiday”.  I have never checked into it but I have to think Valentine’s Day is one of the biggest revenue times for the card – and flower and chocolate industry.  Every year mostly males it seems race around on February 12th  or 13th  ordering flowers, picking out cards and chocolates.  So this year I am providing a public service announcement to all the procrastinators – you still have several days left.  Get out there early and get your sweetheart something.  And have a Happy Valentine’s Day.

 

Last week we covered the grand daddy of the greeks – delta.  This week we will touch on its multiple personality cousin – gamma.  As we remember from last week, delta is how much an option price changes with a $1 movement in the underlying.  Calls with a delta of 60 will move $.60 for every $1 movement in the underlying.  Deltas are based on the relative relationship between the option strike price and the underlying.  As the underlying moves, deltas move as well.  The rate of change of delta with a $1 movement in the underlying is referred to as gamma.  If delta can be thought of the speed that option prices change, gamma can be thought as the acceleration.  For example, an ABC Call has a delta of 40 with the stock price at $50.  If the stock moves up $1 to $51 the delta of the call is now say 42.  This is because the call now is getting closer to being in the money.  Gamma measures the rate of change of the delta move from 40 to 42.  The higher the rate of change, the higher the gamma.  The closer an option is to the at the money strike, the greater the gamma.  As we move farther away from the at the money, either in the money or out of the money, the lower the gamma.  For an option that is deep in the money with a delta of 99, that delta will move very little  with a $1 move in the underlying since the probability of finishing in the money is still very high.  And a delta for a far out of the money option will move very little with that $1 move as it still is highly unlikely it will finish in the money.  The at the money options have less certainty of finishing in or out of the money so delta moves more with a given move in the underlying, hence greater gamma.  There are other factors that affect gamma as well such as time and implied volatility.  Increased implied volatility tends to lower gamma near the at the money and raise gamma for the strikes farther away.  Time acts in the same way as implied volatility, lowering at the money and raising farther removed strikes.  Next week – theta.

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