What is the Best Underlying Price to Price Options?

What is the Best Underlying Price to Price Options?

The two big unknowns in pricing an option are implied volatility and the underlying price. Much time and effort is spent modeling implied volatility, and rightly so, for it is an important source of trading edge and long-term profitability. However, relatively little effort is spent thinking about the underlying price.  Over short-time scales, getting the underlying price “right” may be just as important, if not more so, than capturing changes in implied volatility.

Think about this for a moment. In the “seconds” timeframe, what is more volatile – volatility or the underlying price? What is more likely to cause a market maker to refresh or pull his or her quotes?

I would think for most actively traded options the answer is the underlying price.

It makes sense then that an option trader should spend some time and effort thinking about what the right underlying price should be. This is especially salient as markets are becoming more and more sophisticated and speed and agility are becoming increasingly important in capturing option trading edge.

What then is the “right” underlying price to use to price an option?

You might say that’s easy. If I am buying a call or selling a put (buying deltas), it would be the bid price of the underlying; and if I am selling a call or buying a put (selling deltas), it would be the ask price of the underlying.

This may be the price that one might receive from a hedge, but it is not necessarily the best price one could receive. In fact, in many market conditions, the assumption that one could hit the bid or ask to complete his or her hedge is clearly wrong.

In most scenarios, there is a better price called a micro-price that more accurately reflects the true value of the underlying. A well constructed micro-price will more frequently pull a market makers quote when the market is poised to move against it and will position his or her option prices more advantageously in favorable situations. It can do this because micro-price models process information more efficiently; they act as a source of hidden computational speed and allow trading systems to react more quickly to changing market conditions.

The micro-price is the “right” price to use to price an option.

How do micro-price models do this?

In a nutshell, most micro-price models incorporate the current trading dynamics of an instrument and create a short-term forecast of this instrument.

To illustrate the power of adding a micro-price model to your option theoretical value calculations, let’s start with a rather basic situation where the near month WTI Crude Futures (CL) is currently

ScottMorris1

Intuitively, there is not much in this market structure to help us predict whether the next futures move is more likely to go up or go down. If we had to guess one price to represent the value of CL, we would likely default to the midpoint of the bid and ask of 92.525 and use the current bid and ask to price our options. We cannot do any better.

Now let’s assume that a very short time later, the size of the ask is reduced from 41 to only 2 contracts:

ScottMorris2

Do we still feel the same? Probably not, for only a 2 lot buy market order is needed to push the ask to 92.54.

We are probably as equally likely to see the market move to something like:

ScottMorris3

than to see it revert to where we began. Thus, if we had to pick one price to represent the value of CL, it would probably be a value greater than the midpoint and closer to 92.53, and since there is a pretty good chance the ask is likely to move up to 92.54, we may want to reconsider a higher ask price when pricing our theoreticals.

Micro-price models incorporate this intuition directly into the theoretical value generation process.

Here is a “real” example that illustrates the power of a micro-price model. The data in the graph below are again for the WTI Crude Futures and represent a 15.5 second window of the OptionsCity real-time datafeed:

scott_Morris_BLOG1

Notice in the first section of the graph, when the market was 92.74 x 92.75, how the microPrice (the blue line) is trending up just before the actual bid and ask moves higher. Please note that each observation is based on the arrival time of the data and, thus, the observations are not evenly spaced in time. However, it is safe to say that at least 200 to 300 milliseconds before the price change, the microPrice had correctly predicted the event.  Each additional section of the graph, to different degrees, shows a similar pattern. The statistics behind the forecast are quite strong (especially for financial time-series), but like all statistical models, they are not perfect.

The driver for this model is a simple regression model that I have optimized directly from the OptionsCity real-time datafeed. The model optimized a beta coefficient related to the ratio of the bidSize and askSize (sizeRatio):

microPrice = midpoint + f(Beta, sizeRatio)

The next graph shows just how the sizeRatio drives the microPrice adjustment. The purple chart line (right axis) represents the sizeRatio where a value between .5 and 1.0 represents less ask size than bid size, and the closer to 1.0 the more extreme this ratio.

scott_morris_Blob2

If we return our analysis to the first segment of the graph, we can clearly see that as sizeRatio gets closer to 1.0 (in this case the ask is getting smaller and smaller), the microPrice is rising to reflect the increased probability that the market jumps to the next tick increment.

Summary

The above exercise certainly is not rocket science, but I hope it has illustrated that one should not take “as given” the underlying price used to price his or her options. With some simple intuition and a little quantitative rigor, additional market-making edge can be obtained by incorporating a micro-pricing model into your theoretical value calculations.

Micro-price models can:

  • Adjust prices faster to reduce pick-off risk.
  • Adjust prices faster to improve queue placement.
  • Allow a market maker to make tighter markets and reap more trading edge.

Implicit in all three of these advantages is a real sense of enhanced speed and better system performance.

And we have only begun to scratch the surface.

On February 4th I will be participating in an OptionsCity Webinar, Smarter Market Making: Predicting Underlyings From Market Microstructure. Join me to learn about a similar, but more powerful, model, FastFutures, which will be debuting on the OptionsCity AlgoStore.

R. Scott Morris

Morris Consulting, LLC

scott@rscottmorrisconsulting.com

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