Sunday, February 6, 2022

Gamma and Gamma Exposure—Knowing the Basics

In 2021, $SPX options make up 16% of the $SPX market cap.  To hedge a book of $SPX options, the primary risk-management technique is delta hedging, which is when option traders start messing about in the equity markets. 

Some may recall the Gamestop ($GME) saga that took place earlier this year - Much of this bizarre and explosive move was attributed to Gamma Exposure (GEX), which was a prime example of how the mechanics of gamma exposure can influence market action in a very powerful way.
 
Chart 1.  Estimated SPX Dealer Gamma Exposure - All Expirations (Source: @t1alpha)


Option Greeks

 

An option's price can be influenced by a number of factors that can either help or hurt traders depending on the type of positions they have taken.[1]

Successful traders understand the factors that influence options pricing, which include the so-called "Greeks"—a set of risk measures so named after the Greek letters that denote them, which indicate how sensitive an option is to time-value decay, changes in implied volatility, and movements in the price of its underlying security. For example, two of the four Greeks are:

Delta—is a measure of the change in an option's price or premium resulting from a change in the underlying asset.

Gamma—measures delta's rate of change over time, as well as the rate of change in the underlying asset. Gamma helps forecast price moves in the underlying asset.


Delta Hedging

 

In general, hedging is a strategy used to reduce risk. An investor hedges a position in a particular security to minimize the chance of a loss. The nature of a hedge, though, also means the investor will give up potential gains as well.

Delta hedging is a strategy in which an investor hedges the risk of a price fluctuation in an option by taking an offsetting position in the underlying security (stocks or futures).
To initiate a delta hedge you need to first understand what delta is, how it works, and know the delta value for the option you hold.[4]
Assume a call option has a delta of 0.5. That means the price of the call option will increase by 50 cents for every $1 increase in the price of the underlying stock that the call option is written on. Now suppose you have purchased a call option on that stock for $5 and the price of the stock is $60. If the stock’s price rises to $65, then the options price will rise to $7.50.

An investor can hedge delta risk, for example, by buying the call option, then short-selling the underlying stock. The amount of the underlying stock that must be sold to exactly offset the delta risk is based on the delta..[5]

If the delta is 0.5, then the investor needs to sell half of the number of securities that are covered by the call option contract. Since a typical option contract covers 100 shares of the underlying security, the investor would need to short 50 shares of the underlying stock to have a delta-neutral position.

The amount of delta-hedging needed is mainly dependent on this thing called gamma. 


How to Find Spot Gamma?

 

In our daily observations of (bizarre) market moves, we frequently analyze the delta-hedging of option positions by dealers (or market makers), i.e. gamma, which has emerged as one of the dominant drivers of risk assets. But why is gamma important, especially in option-expiration weeks? 

Gamma has the potential to be one of the most important non-fundamental flows in equity markets (particularly when “short gamma” causes volatility to accelerate), but tracking gamma is complex and dynamic..[6]

You can find out spot gamma which shows the gamma exposure at the current spot level in 2 ways:

  • Provided by Option Chain (e.g. CBOE)
    • Sometimes it's provided on the option chain, along with implied volatility (IV) and deltas.
  • Otherwise
    • Need to calculate it manually (see the section "How to Construct Spot Gamma Using Excel?" below)

 

Chart 2.  Gamma Exposure Profile, $SPX (02/01/2022; Source: @perfiliev)

Gamma Exposure Profile

 
Our goal here is to find out two things:
  1. How much gamma the dealers are sitting on across the index levels
  2. What's their current total gamma exposure

In Chart 2, it shows an approximate amount of dealer hedging flows across index levels:

Two levels are notable on this chart:

  1. Current Spot Gamma Exposure—where Total Gamma Exposure blue line crosses the current spot red line
    • Occurs at around -$19Bn in this chart and it means that Option dealers need to SELL $19Bn worth of $SPX index for each 1% move DOWN, and BUY $19Bn for each 1% move UP.
  2. Zero Gamma Level (or Gamma Flip)—where Total Gamma Exposure blue line crosses zero
    • On the chart, it occurs at around 4,574 $SPX level. This is the Zero Gamma level, where the dealer gamma exposure flips from positive to negative.  
    • Above this level, dealer hedging flows are stabilizing and add liquidity to the market. Below this level, dealer hedging flows are destabilizing and add to the volatility instead. 
    • At this level, flows are zero, as delta doesn't need re-balancing due to spot moves.  

You can read [8] to understand more on "What is Gamma, Market Gamma and/or Total Market Gamma?".

 

How to Construct Spot Gamma Using Excel?


To construct spot gamma, you need:[2]
  • Options data
    • Strikes, expiries, and open interest (OI) are needed
    • For US stocks, CBOE provide their delayed quotes (link).
      • Search for "SPX" → click on Options tab → set Options Range = All → set Expiration = All → click View Chain
      • To download the entire options chain, scroll all the way down, and click on Download CSV.
      • Note that open interest figures are updated once per day and it's better to download them during market hours. 
  • Excel
    • First, we need to calculate the unit gamma for each option and then sum them up across strikes and expiries

But, you also need to make the below assumptions:
  • On an index level
    • The dealers are long the calls and short the puts and we'll assume that calls carry positive gamma and puts negative
  • On single-stocks
    • It's more debatable as the street can be short the calls due to some speculative buying frenzy
For details, please follow Sergei Perfiliev's article..[2]

References

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