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It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black-Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/n in the case of usual binomial models since the second term (in 1/ √ n) vanishes. The next term is of type C 2 (n)/n, with C 2 (n) some explicit bounded function of n that has no limit when n tends to infinity.

A novel method for paralytic shellfish poisoning (PSP) toxins which is based on the chromatographic separation of the toxins using a zwitterionic (ZIC) hydrophilic interaction chromatography (HILIC) column is presented. Efficient retention of the polar PSP toxins on the ZIC-HILIC column allowed their selective and sensitive determination by the application of mass spectrometric (MS/MS) detection or as derivatives after oxidation prior to fluorescence detection (FD). Low buffer concentrations and the omission of ion-pair reagents decreased the limits of detection (LODs) by MS/MS analysis and showed a good linearity for both methods of detection. This method can be applied for the qualitative and quantitative determination of PSP toxins in various types of phytoplankton, and for the routine analysis of seafood.

Tetrodotoxin (TTX) and its analogs (TTXs), widely distributed among marine as well as terrestrial animals, induce dangerous intoxications. These highly potential toxins are also known as the causative agent of puffer fish poisoning. A newly developed highly sensitive method for determination of TTXs based on hydrophilic interaction chromatography and mass-spectrometric detection is presented. TTX, anhydrotetrodotoxin, 11-deoxytetrodotoxin and trideoxytetrodotoxin were determined in separated tissues of Bangladeshi marine puffers, Takifugu oblongus. TTX was predominant in skin, muscle and liver, whereas trideoxytetrodotoxin preponderated in the ovary. The toxicity of the various tissues was determined by a mouse bioassay.