Are Jumps in Stock Returns Diversifiable? Evidence and Implications for Option Pricing

On Time-scaling of Risk and the Square-root-of-time Rule

“…Most research in option pricing follows Merton by assuming that the jump component is non-system(at)ic, but more recently several authors have argued that in order to better understand the data, and in particular option prices, the system(at)ic aspect of jumps needs to be considered (see e.g. Jarrow and Rosenfeld, 1984;Naik and Lee, 1990;Schwert, 1990;Kim et al, 1994;Bakshi et al, 1997). In particular the substantially negatively skewed implied distribution of post-'87 out-of-the money put options would call for a jumpdiffusion model, possibly in conjunction with stochastic volatility.…”

Detecting volatility changes across the oil sector

“…Kim, Oh, and Brooks ( 1994) find evidence that sudden volatility changes in common stock prices are systematic in nature, that is, nondiversifiable, which can jeopardize the use of a hedging strategy.…”

A simulation environment for discontinuous portfolio value processes

“…We describe in the sequel and in the following section the parameter set for unstable markets, de"ning and then extending an initial maximum likelihood estimate for the return process (1) [8] (see Appendix A), and then deriving the associated portfolio dynamics. Consider the following transformation of (1) based on the introduction of the compensated Poisson process q R :…”

“…equation (8)}displaying in Figure 1, the mean, plus/minus the standard deviation, and the worst and best scenarios, over four test periods, and back testing the model output with respect to actual market performance. The last two test problems do cover the two business weeks starting on 31 July and 14 August, right before the crisis.…”

“…The maximum likelihood procedure is based on the de"nition of a mixed Gaussian}Poisson probability distribution [8] for the risky index return process and the maximization of the associated likelihood function using for double-check both a quasi-Newton algorithm and a reduced gradient algorithm.…”