文件名称:
Two stock options at the races Black–Scholes forecasts
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上传时间: 2014-02-24
详细说明： Suppose one buys two very similar stocks and is curious about how much after some time T one of them will contribute to the overall asset expecting of course that it should be around 1 2 of the sum Here we examine this question within the classical Black and Scholes BS model focusing on the evolution of the probability density function P w of a random variable w a 1 T a 1 T + a 2 T where a 1 T and a 2 T are the values of two either European or the Asian style options produced by two absolutely iden tical BS stochastic equations We show that within the realm of the BS model the behavior of P w is surprisingly different from common sense based expectations For the Europeanstyle options P w always undergoes a transition when T approaches a certain threshold value from a unimodal to a bimodal form with the most probable values being close to 0 and 1 and strikingly w 1 2 being the least probable value This signifies that the symmetry between two options spontaneously breaks and just one of them completely dominates the sum For path dependent Asian style options we observe the same anomalous behavior but only for a certain range of parameters Outside of this range P w is always a bell shaped function with a maximum at w 1 2 Introduction">Suppose one buys two very similar stocks and is curious about how much after some time T one of them will contribute to the overall asset expecting of course that it should be around 1 2 of the sum Here we examine this question within the classical Black and Scholes BS model focusing on th [更多] ...展开收缩
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