Thursday, May 5, 2011

Volatility: How to Measure It*

Prices for oil, like those of many other commodities, are inherently volatile. In recent years, the oil market has been characterised by rising, and at times, rapidly fluctuating, price levels. In the last six months alone, oil prices have fluctuated in a wide range from $75/bbl to $125/bbl.

The concept of volatility may itself at times be confused simply with rising prices; however, volatility can equally result in prices that are significantly lower than historical average levels. Volatility is the term used in finance for the day-to-day, week-to-week, month-to-month or year-to-year variation in asset or commodity prices. It measures how much a price changes either about its constant long-term level, or about a long-term trend. That is to say, volatility measures variability, or dispersion about a central tendency. In this respect, it is important to note that volatility does not measure the direction of price changes; rather it measures dispersion of prices about the mean. It is also very common to refer to returns’ volatility when we talk about volatility of a commodity price.
The apparent increased volatility of oil prices raises questions about the determinants of volatility in oil markets. Since oil is considered to have highly inelastic supply and demand curves at least in the short run, neither supply nor demand initially responds much to price changes. Therefore, any shock to supply or demand will lead to large changes in oil prices. The dissemination of new information related to fundamentals results in price adjustment as market participants evaluate the implications of this information. It is further argued that emergence of a new class of financial traders has transformed the oil market substantially to a more volatile market. However, most research shows that the increase in financial participations in the oil market can be explained by the rise in volatility, not the other way around.
Two other caveats are perhaps worth mentioning: Firstly, it can be observed that during the so-called ‘golden age’ of lower prices in the 1990s, volatility as measured by absolute mean returns was at times markedly higher than in recent years, even allowing for an almost unprecedented economic recession. Secondly, the drivers of market volatility can be very different when comparing the short term and medium to longer term.  For the latter, cyclical macroeconomic factors, more than supply/demand shocks, are a key driver.
There are various ways to measure volatility. However, we can split volatility models into two parts: historical volatility and implied volatility. Historical volatility models use time series of past market prices while implied volatility uses traded option prices. Therefore, we can say that historical volatility is backward looking while implied volatility is a forward looking measure of volatility.
Historical Volatility
Historical volatility looks at past behaviour of price movement and measures the variation in the price. One such measure is the standard deviation. Standard deviation (σ) is computed from a set of historical data as

where R is the return calculated as the natural log of daily price changes in the price of the underlying asset and µ  is the mean return during the lookback period. The choice of price and lookback period gives rise to different estimations of volatility. In general, close-to-close prices are used but some prefer to use open-to-close prices to calculate return. The lookback period also has important implications for volatility. The historical average method uses all historical data available. The moving average method, on the other hand, discards some older observations.  The exponentially weighted moving average method uses only more recent observations.
However all techniques have shortcomings. The historical average methodology gives equal weight to all observations regardless of relevance today. Although the moving average estimation technique provides some information on the evolution of volatility, it suffers from assigning an equal weight to all observations in the estimation window and zero weight to older observations. It also raises the issue of window-length determination. On the one hand, if the window is too narrow, one runs the risk of ignoring important observations in the data by giving zero weight to these observations. On the other hand, if the window is too wide, old observations will be given weight even though they may not be relevant to the analysis. To overcome these problems, exponential smoothing techniques assign declining weights to older observations based on a smoothing parameter without any prior determination on the amount of past data to be used in the analysis. One drawback of this second approach is that the user must adopt an ad hoc approach to choose the smoothing parameter.
Apart from standard deviations based volatility, researchers also use model-free daily squared return and absolute return as a proxy for daily volatility. Range-based volatility estimation, calculated using market daily high and low prices, is another methodology adopted to calculate volatility. Although it is very easy to calculate, it is also very sensitive to outliers.
The empirical observation that volatility is not constant over time and that it has memory has led to more sophisticated time series models, known as ARCH/GARCH models. These models capture volatility persistence, time-varying mean as well as the non-constant nature of volatility. ARCH/GARCH type models do not make use of unconditional variance rather they estimate conditional variance. Since conditional variance at time t is known at time t-1 by construction, it provides one-step ahead forecast. However, the inability of latent volatility models like ARCH/GARCH to describe satisfactorily several stylised facts that are observed in financial markets has led to realized volatility models, where  volatility is estimated using high frequency intra-daily data. Realised volatility is calculated using squared returns at short intervals (either time or tick). However, realised volatility measures constructed with high frequency data can be biased by market microstructure noise. Therefore, recent research has focused on minimising the microstructure noise inherent in these models.
Implied Volatility
As opposed to historical volatility measures, implied volatility does not depend on historical prices. Instead, it depends on a particular model of the relationship between price and volatility. A simple option-pricing model, such as Black-Scholes, will give a theoretical price for an option as a function of implicit parameters, such as the strike price, risk free interest rate, time to maturity, spot price, dividend and volatility. With the exception of volatility, all other parameters are either given or can be observed. However, we observe option prices in the market place. The implied volatility of an option is the volatility for which the Black-Scholes (or any other particular model) price equals the market price. That is to say, there is a one-to-one correspondence between prices and implied volatility. Implied volatilities are used to gauge a market’s expectation about future volatility. Therefore, implied volatilities are forward looking as opposed to historical volatilities.
Accurate measures of volatility are important for understanding the functioning of markets. Estimated volatilities vary based on methodology, time period chosen and time horizon (intra-daily, daily, weekly, monthly, or annual). Oil Medium Term report in June will provide in-depth analysis of observed volatility in the oil market during the last decade.

*IEA Oil Market report April-2011

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