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To capture the impact of skewness and increase kurtosis on Black’s  European put values, we first substitute a Gram-Charlier (GC) distribution and next a Johnson distribution for Black’s Gaussian one. We introduce next each distribution in the option payoff and develop until the closedform expression of each put is arrived at. Finally, we estimate by simulations GC, Johnson and Black put options, choosing the latter one as benchmark. Simulation estimates encompassing both skewness and kurtosis show that, for at-the-money (ATM) or slightly in-the-money put values, 1) Black’s overvaluation with respect to Johnson puts is very significant and 2) its undervaluation with respect to GC ones remains moderate. Yet, by using the same skewness values for both GC and Johnson puts, we highlight the differences induced by increasing kurtosis between the two models. In this case, the GC overvaluation for ATM values is explained by value differences in the put time component. Yet, while both Black and GC values exhibit significant time decay close to expiry, Johnson’s ones remain stable up to maturity.
Time series for the Southern Oscillation Index and mean global near surface temperature anomalies are compared for the 1950 to 2012 period using recently released HadCRU4 data. The method avoids a focused statistical analysis of the data, in part because the study deals with smoothed data, which means there is the danger of spurious correlations, and in part because the El Ni?o Southern Oscillation is a cyclical phenomenon of irregular period. In these situations the results of regression analysis or similar statistical evaluation can be misleading. With the potential controversy arising over a particular statistical analysis removed, the findings indicate that El Nino-Southern Oscillation exercises a major influence on mean global temperature. The results show the potential of natural forcing mechanisms to account for mean global temperature variation, although the extent of the influence is difficult to quantify from among the variability of short-term influences.