How the limit order book became abstracted into options and why gamma exposure matters

Information obtained from a thread courtesy of squeezemetrics via Twitter

You know how old-school traders talk about using the limit order book to know where supply and demand are? Basically what happened is that the limit order book got abstracted into options, and the actual buying and selling is now done by option dealers, on behalf of customers.

So what happens is, I sell a call because I want to collect some premium and give up some upside. This is largely equivalent to submitting a bunch of progressively larger limit sell orders above the market, except that those orders cannot be seen.

So what happens is that the option dealer takes the other side of those would-be limit orders by shorting the underlying and committing to, in this case, a schedule of buying the underlying when it goes down, and selling more when it goes up.

This means that there are, through the agency of the option dealer, a bunch of what are effectively limit orders sitting above and below the market, all of which will push against any move in the underlying itself. The more of these there are, the more stifling it gets.

So when GEX is really high, that’s when it’s super-stifling. BUT WAIT THERE’S MORE. As these call options lose value, the dealer slowly buys back some of the underlying that they shorted before, slowly supporting the market, ceteris paribus. Low volatility, upside drift.

(Hopefully it’s obvious why knowing where supply and demand will be is useful.)

What are the options Greeks?

This article is part of a more broad series of research questions I address regarding Gamma Exposure. Check out this post for more.

Greeks refer to dimension of risk that an options position entails. The Greeks are used by options traders and portfolio managers to hedge different risks to their positions.

Is simple terms, the Greeks are derived based off a pricing model, like Black-Scholes, using inputs: option price, underlying stock price, days to expiration, and risk free interest rate.

The most commonly used Greeks used are Delta, Gamma, Theta, Vega.

Delta

Delta is the amount an option price is expected to move based on a $1 change in the underlying stock.

Calls always have positive delta, between 0 and 1. If the underlying stock price goes up and no other variables change, the price for the call will go up.

If a call has a delta of 0.50 and the stock goes up $1, the price of the call will go up about $.50. If the stock goes down $1, the price of the call will go down about $.50.

Puts always have a negative delta, between 0 and -1.

Gamma

Gamma is the rate of change in delta for every $1 change in the stock price. If delta is the “speed” at which option prices change, you can think of gamma as the “acceleration.”

Options with the highest gamma are the most responsive to changes in the price of the underlying stock.

Gamma is highest for options with strike prices near the current underlying stock price. It is also highest for those options at the money that are closer to expiring vs. those options which are due to expire further out in the future.

Theta

Theta, aka time decay an option buyer’s biggest enemy, and option seller’s best friend. Theta is the amount the price of calls and puts will decrease theoretically for a one-day change in the time to expiration.

In the options market, the passage of time will erode an options value. Time value melts away and does so at an accelerated rate as expiration approaches.

Vega

Vega is the amount call and put prices will change, in theory, for a corresponding one-point change in implied volatility.

Vega does not have any effect on the intrinsic value of options, it only affects the “time value” of an option’s price.

Typically, as implied volatility increases, the value of options will increase. That’s because an increase in implied volatility suggests an increased range of potential movement for the stock.

Conclusion

If you’re trading options, you absolutely must understand those Greeks above and how they impact your trading strategies.

What is delta hedging? How does this influence option market makers’ gamma exposure?

This article is part of a more broad series of research questions I address regarding Gamma Exposure. Check out this post for more.

Market makers are exposed to risks in the market and continuously protect themselves against these risks. One way they they manage risk is by remaining delta neutral on their portfolio. This is called delta hedging.

Example

Say you wish to buy one call option on SPY which has a delta value of 0.45. The market makers, who took your order, will have the opposite position of a -0.45 delta.

When the market maker sells you that call option, they can immediately hedge against their -0.45 delta by buying one call option on SPY with a 0.45 delta OR by buying 45 stocks, (which always have a delta of 1).

For the purposes of gamma exposure, we make the assumption that the market makers are hedging their trades by buying stocks in the underlying instrument.

What is gamma in risk management? How do you hedge gamma?

Gamma is a risk to the market maker when the markets are moving drastically in one direction. Gamma hedging is done to protect the dealer from larger than expected moves in the underlying options contract.

Gamma is the convexity of an options position, and is never get hedged away immediately. By continuously hedging delta risks, dealers hope to limit their exposure to large moves in the stock.

Example

To go along with the example above, let’s assume the dealer gamma has a value of -0.05.

Say your call position moves up $1, and now on the market makers book, they have a delta of -0.50, down from -0.45. The dealer would look to sell 5 more shares of the stock. The gamma was at -0.05 and the underlying price moved up by $1, and this caused the delta on their books became more negative by this -0.05 amount.

If the call position moves down $1, from a delta of -0.45 down to -0.40 on the dealers books, then the dealer would look to buy 5 shares of the stock.

It is this simple (theoretical) illustration that shows the activity of market makers (dealers) that can help you understand the activities of those and how those active rehedging programs can have such a sizable impact on the options and stock market.

Why does gamma exposure suppress or exacerbate stock price movements?

This article is part of a more broad series of research questions I address regarding Gamma Exposure. Check out this post for more.

When gamma exposure is positive, it implies that market makers will hedge their positions in a manner that stifles volatility. It means market makers are selling into highs and buying into lows. They are essentially buying the dip and selling the rip, and keeping volatility low in the process.

When gamma exposure is negative, it implies market makers will hedge their trades in a manner that magnifies the movement of the market. Market makers are now selling into the lows or buying into the highs.

Market makers are buying or selling their stock positions in the same direction with the current market. This is one reason why selloffs can become so deep, and why the swing back after a market selloff is so dramatic.

Much of this has to do with the effect of gamma and how it affects the delta of an options position. The gamma is a measure of the effect a $1 move on the underlying stock will have on delta.

If a market maker has a large gamma exposure value in their option book, then a $1 move in the underlying has a large effect on the delta exposure of a dealers book. This means when gamma is high, you can anticipate large changes in the delta, which the dealer will ultimately hedge against.

What basic assumptions are made in calculating gamma exposure?

This article is part of a more broad series of research questions I address regarding Gamma Exposure. Check out this post for more.

Note below adapted from SqueezeMetrics White Paper

There are a few assumptions we make when we calculate gamma exposure. These are the following assumptions:

All options traded are facilitated by delta-hedgers. We assume that all orders run through a market maker who owns a book of options.

Call options are sold by investors and bought by market makers. Based off skew, open interest at a strike, and effects of GEX, call overwriting drives the options market for calls. We assume call options are written as covered calls for portfolios.

Put options are sold by investors and bought by market makers. Puts are bought by parties looking to protection their portfolios against a drop in market prices.

Based off skew, the implied volatility of put options is generally higher than the implied volatility for call options.

Market makers hedged deltas continuously. This may not be the case, but the assumption is held for the purposes of gamma exposure.

Possible issues for those assumptions above:

If traders and investors are buying more call options than they are selling to market makers, this would drastically change the calculation of gamma exposure. This would also be true if traders and investors are selling more put options than they are buying from market makers.

Like any signal in the market, the gamma exposure signal could go away as it becomes more known. For that reason, gamma exposure should only be used as one component of your decision making process.

Great Resources on Gamma Exposure

This article is part of a more broad series of research questions I address regarding Gamma Exposure. Check out this post for more.

SqueezeMetrics – White Paper on Gamma Exposure

We believe that the greater granularity of the GEX distributions suggests that there is some element of market volatility that is simply not able to be captured by the VIX model, or indeed any other variance metric based on quoted option prices. Rather than prices, GEX concerns itself with the quantity and characteristics of all existing option contracts at all strikes, and at all expirations―and the market participants who trade them.

Conclusion

If investors continue to look toward the option market for alpha signals and risk assessments, they would do well to consider Gamma Exposure as a smarter alternative to price-derived volatility and variance estimates.

The key deficiency in using option prices to gauge future volatility is that no two market-makers’ books are the same, and a tight spread from any one market-maker completely obscures the risk appetite of every other.

This problem is readily ameliorated by computing the GEX of options known to be in circulation and deriving projected return distributions from the historical market impact of those contracts.

And so, when―in light of the evidence―investors eventually acknowledge that the option market does have a truly pervasive, day-to-day impact on the paths and volatilities of stock prices, we think that it is a natural next step to consider GEX an essential addition to the equity investment process.

SqueezeMetrics – Documentation

Gamma exposure (GEX); refers to the sensitivity of existing option contracts to changes in the underlying price. Like with DPI, substantial imbalances can occur between market-makers’ call- and put-option exposures, and when those imbalances occur, the effect of their hedges can either accelerate price swings (like a squeeze) or stifle movement entirely.

We have developed a novel way to quantify this exposure and the direction of hedging that occurs in the event of n% price moves. The effect of this insight on our forecasting has been profound.

SqueezeMetrics – Monitor

This monitor by SqueezeMetrics will provide you with Dark Pool buying as well as Gamma Exposure for all of the components of the S&P 500. (Please note, this is NOT Gamma Exposure on the S&P 500 index (SPX) itself. Rather it is a calculation of all of the component stocks on the S&P 500. For SPX GEX, you can subscribe to SqueezeMetrics or find that information at TradingVolatility below.)

Trading Volatility – GEX Charts

Gamma Exposure Charts

A view of the cumulative Gamma Exposure (in $) across each strike for a given stock, calculated using all options with less than 94 days to expiration.

Spot Gamma – Updated Tables on Gamma by Strike and by Expiration Date

These options data tables based on open interest produce gamma readings which can be used to define important levels in the S&P500 (SPX) market. This data is recalculated each night based on a proprietary model. Some traders and investors believe that large open interest at a specific options strike produces actionable trading intelligence. These tables are all grouped by strike, not expiration date.

Bookmark this post if you wish. I will be updating it frequently. Consider all my posts to be a work in progress.

If you have other resources with regards to Gamma Exposure, please share them in the comments below!