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According to Prof.Merton,the total change in the stock price is composed of two types of changes,the normal,marginal vibrations and the abnormal,sudden and rare breaks.In order to analyze these marketing behaviors more simply and efficiently,we use the binomial trees to introduce a new method on Valuation of European Contingent Claims in a market in face of sudden and rare breaks (with jumps),on the basis of using binomial trees to investigate the normal changes of financial securities.The explicit formulas of the contingent claims value and the underlying assets prices are given.