## Why volatility?

My professional and academic work has been primarily focused on the topic of volatility. The interested reader will find many of my works related to the volatility. However, there is something I wanted to share between the lines…

Indeed, volatility is an indispensable object in the modern quantitative finance. However, what is volatility? How do we define and measure volatility? How do we model and trade volatility? Once we attempt to answer these questions, we will immediately get into many dilemmas.

For an example, statistically, the volatility measures deviations around the expected or the average value. The first dilemma that we face is whether we aim at estimating the population deviation or the sample deviation. The major obstacle for the statistical estimation using empirical data is that both the number and size of available samples are small and finite. It is very common to draw conclusions from a single sample, but that is not what we should aim at. There is a thin line between estimated deviations that we have observed in sampled data and future realized deviations that we would face in the future.

When applied to the finance, the volatility is commonly referred to as a unit of the risk measuring the deviation of asset returns in the statistical sense. The key dilemma in the finance, especially in investing and trading applications, is whether to use static or dynamic measures of deviations. For an example, when we target 10% volatility of our investment portfolio, what time scale should we use: one hour, day, month, year, or decade? The time scale of our risk horizon is the key to our definition of a measure of the risk, irrespectively whether we apply the volatility to measure our risk or not. Does it really make sense to use a static measure of volatility when our risk horizon is short?

Then, of course, a career-defining dilemma is whether we can trade the volatility? Can we trade the volatility measured over different frequencies? Can we trade the volatility of different assets? Can we trade the volatility implied in option markets? Finally, how can we create an edge in volatility trading?

As a researcher, I have spent more than a decade working on different volatility models. As a practitioner, I have been building systematic models for volatility trading. Still, it is not fully clear to me what the volatility is as the concept. The deeper I go into details, the more I realize that there are many subtleties when I apply different volatility models and their estimation methods in trading applications.

For example, my recent work is devoted to applying machine learning methods for volatility prediction, modelling the volatility of variables with heavy-tailed distributions, and forecasting the cyclical risk of the volatility. On the practical side, I am aspiring to make my volatility trading models profitable yet reliable in all market conditions.

Overall, I am thrilled to study the subject of the volatility, because there is no end in sight for new model development and trading applications. I believe that any systematic trading application, which involves applying the volatility and covariance matrices for making trading decisions and executions, is only feasible using a proper mix of quantitative methods, innovation, and continuous learning. These applications include, apart of trading implied versus realized volatility and minimum variance optimizations, the volatility targeting, the risk-parity.

Finally, although momentum and trend-following strategies do not appear to be connected to the volatility trading on the first sight, the fact is that trend-following strategies do involve trading short-term versus long-term realized volatilities. The key source of the P&L on trend-following strategies are the realized autocorrelations which are closely related to the long-term volatilities.

To summarise, there are a lot of applications that need a reliable estimation of the volatility but we don’t have yet a well-developed concept of how to define and estimate the volatility. It is going to be a long professional journey… Stay in touch for updates!