No abstract

Risk-neutral (RN) and real-world (RW) densities are derived from option prices and risk assumptions, and are compared with densities obtained from historical time series. Two parametric methods that adjust from RN to RW densities are investigated, firstly a CRRA risk aversion transformation and secondly a statistical calibration.Both risk transformations are estimated using likelihood techniques, for two flexible but tractable density families. Results for the FTSE-100 index show that densities derived from option prices have more explanatory power than historical time series.Furthermore, the pricing kernel between RN & RW densities may be more regular than previously reported and a more reasonable risk aversion function is estimated.

We examine contemporaneous jumps (cojumps) among individual stocks and a proxy for the market portfolio. We show, through a Monte Carlo study, that using intraday jump tests and a coexceedance criterion to detect cojumps has a power similar to the cojump test proposed by Bollerslev et al. (2008). However, we also show that we should not expect to detect all common jumps comprising a cojump when using such coexceedance based detection methods. Empirically, we provide evidence of an association between jumps in the market portfolio and cojumps in the underlying stocks. Consistent with our Monte Carlo evidence, moderate numbers of stocks are often detected to be involved in these (systematic) cojumps. Importantly, the results suggest that market-level news is able to generate simultaneous large jumps in individual stocks. We also find evidence of an association between systematic cojumps and Federal Funds Target Rate announcements.

a b s t r a c tWe 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 transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.

Risk-neutral and real-world densities are derived from option prices and risk assumptions, and are compared with historical densities obtained from time series. Two parametric risk-transformations are used to convert risk-neutral densities into real-world densities. Both transformations are estimated by maximizing the likelihood of observed index levels, for two parametric density families. Results for the FTSE-100 index show that parametric densities derived from option prices have more explanatory power than historical densities and higher likelihoods than densities estimated by spline methods. A combination of parametric real-world and historical densities provides the preferred predictive densities.