Volatility models

Definitions

• Volatility is the measure of how much a variable’s value is expected to vary over a time frame based on its prior movement. Formally, volatility is generally measured as the standard deviation or variance between the variable’s value over time.

• In laymen’s terms: If the price of an asset moves up and down rapidly over short time periods, it has high volatility. If the price almost never changes, it has low volatility.

• Volatility is defined according to a time frame - implied volatility refers to forecasted of volatility in the future while realized volatility is current, or historical, volatility.

• Volatility is generally assumed to be constant in many financial models, famously Black-Scholes, but this assumption is not reflected in reality. The volatility of an asset’s volatility is defined as heteroscedasticity. Crypto markets are particularly heteroscedastic.

• Heteroscedasticity and high volatility are defining traits of crypto markets and pose the greatest challenge in porting over traditional financial models for use in crypto markets. The models Concrete utilizes for forecasting volatility are modified to account for extreme market volatility and heteroscedasticity.

Concrete

• Volatility is the primary measure of risk Concrete monitors as it is a central component to forecasting the price action of cryptocurrencies.

Models

Concrete’s primary volatility forecasting models are:

GARCH models

• GARCH (generalized auto-regressive conditional heteroscedasticity) models are widely-used model in financial contexts to forecast volatility (generate implied volatility measurements).

• GARCH models are generally ineffective in their unmodified form (similar to ARIMA models). As such, Concrete ,and most other financial institutions, modify GARCH models according to the characteristics/traits of their relevant assets/markets.

• For more details on Concrete’s specific GARCH model implementations, refer to Concrete’s yellowpaper.

ASVs

• ASVs (asymmetric volatility models) capture the different impacts of positive and negative return shocks on the volatility of asset return.

• The effect that ASVs aim to capture, the leverage effect, describes the phenomenon of markets reacting in a more volatile manner in negative contexts than positive ones.

UVMs

• UVMs (uncertain volatility models) aim to capture/forecast volatility by outputting probability-based band forecasts as opposed to single-value forecasts (as favored by GARCH and others).

• UVMs are generally based off of existing volatility forecasting models with the addition of stochastic function-defined boundaries on upper and lower volatility forecasts outputs.

Root finding models

• Implied voaltilty measurements are forecasts of volatility in the future (defined by a set time frame), In traditional finance, options (and other) markets have considerable volume which ensures a low margin of error for volatility measurements.

• In crypto, there is a lack of option pricing data for European-style options as most volume in crypto is traded via perpetual futures. Perpetual futures do not have a set expiration date and as such, do not lend themselves to implied volatility forecasts.

• Root finding models allow for Concrete to use existing prices in the crypto market for perpetuals to back-calculate the implied volatility measurements used by other crypto participants.