Introduction

When it comes to estimating conditional volatility, financial professionals have a range of methods at their disposal. These methods can be broadly categorized into parametric and non-parametric approaches. Each approach carries its own set of assumptions, advantages, and limitations. In this chapter, we will delve into the intricacies of these two approaches, discussing their differences, suitability in different scenarios, and offering practical insights.

Parametric Approaches

Parametric approaches assume a specific functional form for volatility and its evolution over time. These methods make strong assumptions about the data distribution, often assuming normality, and require parameter estimation. A common parametric method is the Autoregressive Conditional Heteroskedasticity (ARCH) model. ARCH models assume that volatility is a function of past squared returns, with the assumption that higher past returns lead to higher future volatility. A well-known extension is the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, which incorporates lagged volatility terms, allowing for persistence in volatility patterns.

Example: Consider a stock whose returns tend to exhibit higher volatility following periods of extreme positive or negative returns. Using a GARCH model, you can capture this volatility clustering and make more accurate predictions of future volatility.

Non-Parametric Approaches

Non-parametric approaches, on the other hand, do not rely on specific distribution assumptions. These methods are more flexible and adapt to the data without imposing predefined models. One of the prominent non-parametric methods is the Realized Volatility. It aggregates intraday price movements to calculate volatility, offering a data-driven perspective on market dynamics. Another method is the Historical Volatility, which uses past return data without assuming a particular distribution.

Example: Suppose you’re analyzing a commodity market that experiences sudden price movements. Applying the Realized Volatility method, which accounts for intraday fluctuations, can provide a more accurate depiction of market volatility.

Comparison and Contrast

Parametric approaches provide insights into volatility dynamics and can be efficient when their assumptions hold. However, they can be limited by their assumptions and might not capture complex patterns. Non-parametric approaches, while more flexible, can be sensitive to noise and may require more data for accurate estimation. The choice between the two depends on the data characteristics, market conditions, and the desired trade-off between model complexity and accuracy.