Extracting S&P500 and NASDAQ volatility: The Credit Crisis of 2007-2008

In this chapter we use particle filtering methods to estimate volatility and examine volatility dynamics for three financial time series during the early part of the current credit crisis. We compare estimates from a pure stochastic volatility model, a stochastic volatility model with jumps and a Garch model to each other and to the market volatilities implied by actual option prices. Our three time series are daily data for Standard and Poor’s S&P500 index (or simply SP500), the Nasdaq NDX100 index (or simply NASDAQ) and the financial index XLF for 2007. We provide filtered volatility and parameter estimates for; pure stochastic volatility (SV), stochastic volatility jump (SVJ) and a Garch(1,1) model. Sequential model choice is a natural outcome of our application and we show how the evidence in support of the stochastic volatility jump model accumulates over time as market turbulence increases. Our findings have implications for derivative pricing, portfolio and risk management.