We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three...

Risk-neutral (RN) and real-world (RW) densities are derived from option prices and risk assumptions, and are compared with historical densities obtained from time series. Two parametric methods that adjust from RN to RW densities are developed, firstly a CRRA risk aversion transformation and...

Using high frequency intraday returns, we calculate the realized volatility of the USD/GBP, USD/DEM and USD/JPY exchange rates. It is shown that the dynamics of the logarithms of realized volatilities can be captured by either a fractionally integrated long memory model or a short memory ARMA...

Asset price volatility appears to be more persistent than can be captured by individual, short memory, autoregressive or moving average components. Fractional integration offers a very parsimonious and tempting formulation of this long memory property of volatility but other explanations such as...

We compare forecasts of the realized volatility of the pound, mark and yen exchange rates against the dollar, calculated from intraday rates, over horizons ranging from one day to three months. Our forecasts are obtained from a short memory ARMA model, a long memory ARFIMA model, a GARCH model...

Asset price volatility appears to be more persistent than can be captured by individual, short memory, autoregressive or moving average components. Fractional integration offers a very parsimonious and tempting formulation of this long memory property of volatility but other explanations such as...