In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statist...In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.展开更多
We consider the asymptotic probability distribution coagula-tion-fragmentation process in the thermodynamic limit of the size of a reversible random We prove that the distributions of small, medium and the largest clu...We consider the asymptotic probability distribution coagula-tion-fragmentation process in the thermodynamic limit of the size of a reversible random We prove that the distributions of small, medium and the largest clusters converge to Gaussian, Poisson and 0-1 distributions in the supercritical stage （post-gelation）, respectively. We show also that the mutually dependent distributions of clusters will become independent after the occurrence of a gelation transition. Furthermore, it is proved that all the number distributions of clusters are mutually independent at the critical stage （gelation）, but the distributions of medium and the largest clusters are mutually dependent with positive correlation coefficient in the supercritical stage. When the fragmentation strength goes to zero, there will exist only two types of clusters in the process, one type consists of the smallest clusters, the other is the largest one which has a size nearly equal to the volume （total number of units）.展开更多
If a financial derivative can be traded consecutively and its terminal payoffs can be adjusted as the sum of a bounded process and a stationary process,then we can use the moving average of the historical payoffs to f...If a financial derivative can be traded consecutively and its terminal payoffs can be adjusted as the sum of a bounded process and a stationary process,then we can use the moving average of the historical payoffs to forecast and the corresponding errors form a generalised mean reversion process.Thus we can price the financial derivatives by its moving average.One can even possibly get statistical arbitrage from certain derivative pricing.Weparticularly discuss the example of European call options.We show that there is a possibility to get statistical arbitrage from Black-Scholes’s option price.展开更多
When a financial derivative can be traded consecutively and its terminal payoffs can be adjusted into a stationary time series,there might be a statistical arbitrage opportunity even under the efficient market hypothe...When a financial derivative can be traded consecutively and its terminal payoffs can be adjusted into a stationary time series,there might be a statistical arbitrage opportunity even under the efficient market hypothesis.In particular,we show the examples of selling put options of the three major ETFs(Exchange Traded Funds)in the U.S.market.展开更多
基金Partially supported by National Natural Science Foundation of China （Grant No. 10971068）, National Basic Research Program of China （973 Program） （Grant No. 2007CB814904） and Key Subject Construction Project of Shanghai Education Commission （Grant No. J51601）
文摘In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.
文摘We consider the asymptotic probability distribution coagula-tion-fragmentation process in the thermodynamic limit of the size of a reversible random We prove that the distributions of small, medium and the largest clusters converge to Gaussian, Poisson and 0-1 distributions in the supercritical stage （post-gelation）, respectively. We show also that the mutually dependent distributions of clusters will become independent after the occurrence of a gelation transition. Furthermore, it is proved that all the number distributions of clusters are mutually independent at the critical stage （gelation）, but the distributions of medium and the largest clusters are mutually dependent with positive correlation coefficient in the supercritical stage. When the fragmentation strength goes to zero, there will exist only two types of clusters in the process, one type consists of the smallest clusters, the other is the largest one which has a size nearly equal to the volume （total number of units）.
文摘If a financial derivative can be traded consecutively and its terminal payoffs can be adjusted as the sum of a bounded process and a stationary process,then we can use the moving average of the historical payoffs to forecast and the corresponding errors form a generalised mean reversion process.Thus we can price the financial derivatives by its moving average.One can even possibly get statistical arbitrage from certain derivative pricing.Weparticularly discuss the example of European call options.We show that there is a possibility to get statistical arbitrage from Black-Scholes’s option price.
文摘When a financial derivative can be traded consecutively and its terminal payoffs can be adjusted into a stationary time series,there might be a statistical arbitrage opportunity even under the efficient market hypothesis.In particular,we show the examples of selling put options of the three major ETFs(Exchange Traded Funds)in the U.S.market.
