“Sigma” vol is familiar and easy but has important flaws.
“Sigma” type volatility metrics that rely on assumptions of normally, independent, identically distributed returns have many shortcomings when applied to financial markets, including:
-
- It is well documented that returns very close to the average and at far extremes are experienced more frequently in financial markets than the normal distribution would dictate.
- Sigma is a deterministic measure of price volatility. It does not vary with ticker price or time horizon. This is a major flaw in the Nobel Prize winning and still widely used Black-Scholes option pricing formula, which uses Sigma for its measure of volatility . In contrast, observed option price implied volatility is not constant across strike prices and terms to expiration. There is also often a skew in the implied vol smile, with implied vol typically higher for puts than calls.
More realistic, established vol models are challenging to implement.
Sigma’s shortcomings have for decades motivated the creation of many flavors of “local volatility” and “stochastic” volatility models. These models require solving differential equations for many parameters, or running extensive simulations of them.
Stochastic volatility models are broadly believed to be more robust than local volatility models. They typically include explicit parameters for the items listed below:
-
- mean reversion of volatility (ex: Hurst exponent)
- correlation of volatility with price returns
- volatility jump magnitude and frequency
- volatilty of volatility
- underlying asset drift
VecViz uses Support and Resistance to generate realistic vol metrics
VecViz’s Vector Model includes none of these parameters, nor does it require solving differential equations or extensive monte carlo simulation. Nevertheless, it produces price probability estimates that reflect volatility as price level and time horizon dependent, and capable of clustering, consistent with the parameterization of stochastic volatility models, as depicted in the charts below.
The irregularity of Tops and Bottoms flows through to the distribution of Vector Strength, which in turn flows through to the Vector Model’s price probability percentiles.
The variable topography of the Vector Strength histogram, with some price zones possessing high concentration of Vector Strength and some zones possessing little to none is responsible for a large part of the “stochastic” behavior of the Vector Model price probability percentiles.
Extensive machine learning training of vector based chart shape profiles on horizon specific forward price movement (scaled in terms of Vector Strength traversed) also contributes to this behavior. In other words, some chart shapes allow not just for more upside or downside in terms of Vector Strength than others, some allow for more of that potential upside or downside to occur sooner rather than later.
The Vector Model possesses many of the desirable attributes of stochastic vol, while providing greater accessibility.
Here we have attempted to make the case that the Vector Model’s probability estimates possess attributes of stochastic volatility, despite not using conventional stochastic volatility parameters. We make no claims regarding the quality of the Vector Model’s estimates relative to what is possible with stochastic volatility methods. Such claims would be well beyond our abilities to support with related analysis, as there are many variations to test, and each, to our knowledge, requires significant expert judgement.
That said, we believe the Vector Model’s stochastic-esque perspective on volatility can be of interest to investors that have no access to non-sigma vol analytics, and also to those that do but are interested in getting a different, perhaps more cognitively accessible perspective.