Under Black-Scholes (BS) assumptions, empirical volatility and risk neutral volatility are given by a single parameter, which captures all aspects of risk. Inverting the model to extract implied volatility from an option's market price gives the market's forecast of future empirical volatility....

The recent increase in the national homicide rate in the United States has generated much speculation about its causes among the media. In this article we show how two data visualization tools, funnel charts and time series fan charts, can show the typical volatility in homicide rates in...