Introduction

In the realm of volatility measurement, understanding the differences between conditional and unconditional distributions is essential. These distributions provide distinct perspectives on the variability of asset returns over time. Additionally, the presence of regime switching adds complexity to volatility estimation, as different market regimes can significantly impact volatility dynamics. In this chapter, we delve into the nuances of conditional and unconditional distributions, and examine how regime switching influences volatility quantification.

Conditional and Unconditional Distributions

Conditional distribution refers to the probability distribution of an asset’s return given the information available up to a certain point in time. It captures the changing nature of volatility as new information becomes available. Unconditional distribution, on the other hand, represents the overall probability distribution of asset returns without considering any specific time period or information set. The key distinction lies in whether the distribution considers the historical context or is agnostic to it.

Example: Consider a stock’s daily returns over a year. The conditional distribution would focus on the probability of returns given the information available up to each day. In contrast, the unconditional distribution would consider the entire year’s returns as a whole, without any specific time frame.

Implications of Regime Switching on Volatility

Regime switching refers to the phenomenon where market conditions transition between different states, each with distinct characteristics. These shifts can affect volatility levels and dynamics. For instance, during stable market periods, volatility might be lower, while during periods of economic turmoil or market shocks, volatility could increase significantly. Accurate volatility estimation must account for these regime shifts.

Example: Consider a financial market that alternates between bullish and bearish periods. Bullish periods might exhibit lower volatility due to investor confidence, while bearish periods might experience higher volatility due to uncertainty. If regime shifts are not considered, volatility estimates might be skewed or fail to capture significant changes in market dynamics.