A relativistic way of interpreting an implied volatility curve

12/05/2020

As shown by Albert Einstein through his General Relativity Theory, gravity is the warping of space and time. It is the curvature of the universe, caused by massive bodies, which determines the path that objects travel.

Throughout my career as an option trader, mostly focused on options on domestically traded shares of the Brazilian oil company, Petrobras, I could not help to resist drawing a parallel of the work that I do with the relativistic interpretation described above.

Before I go into details, let me quickly explain some details regarding the trading of Petrobras options in Brazil. First, the market is dominated by call options, with a very liquid market on options expiring within 30 days. So, for the purpose of my argument, I will focus specifically on the dynamic of the volatility curve for the short-term call options on this specific stock.

Now, lets consider for the sake of my argument that the price of the underlying security (shares of Petrobras) behaves like a massive object that, instead of warping space-time, it warps the implied volatility curve of the existing call option contracts.

So, lets interpret the chart below as if the yellow ball represents, not only the price of the stock (in this case, at 27 reais), but also a massive object with weight similar to the moon. As we can see through the chart, each call contract has its own volatility with in-the-money contracts trading with higher implied volatility than at-the-money contracts. Note that the implied volatility associated with the at-the-money contract is also higher than some out-of-the money contracts. (This was the actual configuration during a given day in April of this year).

My argument goes as follows:

Just like a massive object warps space-time, so does the price of a stock to its volatility curve.

As time goes by - as we move from 17 days to expiration to, let´s say, 8 days to expiration - the price of the stock, in this analogy, gains weight. It starts behaving as an even more massive object, therefore, warping even more the volatility curve. Observe the following chart:

As times goes by, the price, which in my analogy was as massive as the moon, starts to resemble a heavier object; perhaps something that becomes as massive as the earth. Consequently, the volatility curve (blue line) becomes warped further just like a heavier object does with space time, see red line below:

By the time that we get very close to expiration date, the curve will be warped enough so that an image that resembles a smile shows up in a clear manner. (see green line)

My argument, however, it is not merely an effort to describe the behavior of the curve. I go further and try to provide investors with some insights into the future behavior of the price of the underlying security in question. There is an insight within this framework that has proven very useful to me throughout my career as an options trader, which goes as follows:

Just like gravity was revealed in 1915 as a geometric phenomenon, the curvature of the volatility as well as the positioning of the price with regards to the lowest level of the curve often proves to be a very good indicator of the future price of the underlying.

In other words, in a market that is neutral to the price direction of the underlying, we should see the price sitting at the low point of the curve. In situations such as the ones I have been describing - where the price is sitting in a position above the low point of the volatility curve - there is a clear bias towards an appreciation of the underlying. The reason for this resides in the fact that the present shape of the curve is most likely due to higher demands for "bull spreads" in relation to the demand for "bear spreads" in the contracts around the current price.

So, if you see a situation such as the one illustrated below, with the current price sitting at 27, while the low point of the curve is at 29, an investor could consider the following investment alternatives:

  • Buy the stock outright, engaging in a directional risk assuming a bias towards further appreciation.
  • Buy call options with exercise price at the low point assuming that, even if the stock price does not go up, these calls may gain value due to an increase in implied volatility (further warping of the curve). Note that this is time sensitive. As time goes by, option premiums decay.
  • An arbitrageur, like myself, may choose to buy call options on the 29 and hedge them by selling at-the-money calls. This transaction, however, should be done maintaining a slightly long delta position.

Well, I could try to provide additional insights, I do not wish to bore you. I hope you find this relativistic analogy not only interesting but useful in trying to use volatility curve as an indicator of future price movements.

Marink Martins

www.myvol.com.br