The summer North Atlantic Oscillation in CMIP3 models and related uncertainties in projected summer drying in Europe

This paper discusses uncertainties in model projections of summer drying in the Euro-Mediterranean region related to errors and uncertainties in the simulation of the summer NAO (SNAO). The SNAO is the leading mode of summer SLP variability in the North Atlantic/European sector and modulates precipitation not only in the vicinity of the SLP dipole (northwest Europe) but also in the Mediterranean region. An analysis of CMIP3 models is conducted to determine the extent to which models reproduce the signature of the SNAO and its impact on precipitation and to assess the role of the SNAO in the projected precipitation reductions. Most models correctly simulate the spatial pattern of the SNAO and the dry anomalies in northwest Europe that accompany the positive phase. The models also capture the concurrent wet conditions in the Mediterranean, but the amplitude of this signal is too weak, especially in the east. This error is related to the poor simulation of the upper-level circulation response to a positive SNAO, namely the observed trough over the Balkans that creates potential instability and favors precipitation. The SNAO is generally projected to trend upwards in CMIP3 models, leading to a consistent signal of precipitation reduction in NW Europe, but the intensity of the trend varies greatly across models, resulting in large uncertainties in the magnitude of the projected drying. In the Mediterranean, because the simulated influence of the SNAO is too weak, no precipitation increase occurs even in the presence of a strong SNAO trend, reducing confidence in these projections.

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.