Distribution and Statistical Behavior of Implied Volatilities

Abstract

In this paper we look at the distribution and statistical behavior of what is known as implied volatilities in the foreign exchange (FX) market. We describe the statistical properties of over-the-counter foreign exchange (OTC FX) options implied at-the-money volatilities. The data set is unique because it presents continuous daily observations of implied volatility. Trying to do the same type of analysis for almost any other option market is very difficult because the data will be “unclean” for this purpose. This is explained in more detail. We find the distribution of implied volatilities has a high peak and fat tails relative to the Gaussian distribution. We also find that the short-term implied volatilities are more volatile than long-term implied volatilities. The data show that the volatility of implied volatility is unstable over time and the correlation between the implied volatilities varies considerably over time. The paper discusses the various implications of these issues. An important question one needs to ask is: What are implied volatilities measuring? The answer to this question is not quite clear in the literature and will affect interpretation of the data.