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如果已知一只股票的历史价格数据，当前价格，希望求未来一段时间后大于某个价格的概率，大概要怎么计算，有几种方法，谢谢

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关键词：历史

Your question is very close to calculating VaR in risk management.

For practical reason, we do not simulate the price directly. Instead, we simulate the return and than convert them back into prices.

The most naive way is that you assue the stock price follows Geometric Brownian Motion. Use the sample standard deviation as sigma and then you can get the solution directly. It is just some simple classical probability work.

Basically, there are two categories for doing so. One is analytical way, which means you assume a distribution for the stock return, and use GARCH model to estimate the volatility via historical data. And than you can either get the analytical solution of the probability you want or you can get the same result by simulation. The most popular distribution for stock returns are Normal and student-t.

The other category is called historical simulation. This is a kind of way in which you do not need to assume the 'true' distribution of the stock return. This category include Historical Simulation (HS), Weighted Historical Simulation (WHS), Filtered Historical Simulation (FHS). You can check these ways online. The basic idea of these methods is just let the data itself 'say' something. Say you use HS, you choose the past 100 day's data and sort them in a ascend way. If you want to find the 60% percentile, you just pick the 60th of the sorted data which means there is 40% percent chance that the stock return will be larger than data 60. WHS and FHS are just make some improvement. The basic idea are the same.

good luck~

我觉得2楼说的很好。补充一下，如果你是为了风险管理（例如算VAR），建议不要用normal或t分布，我不是反对2楼说的“The most popular distribution for stock returns are Normal and student-t”，但那句话适用的情况多半是为PRICING目的，而不是风险管理目的。为风险管理，我推荐2楼说的historical simulation或其他从real-world measure出发的方法（比如找个能更好拟合实际股价变动的分布，更好能拟合实际股价变动的分布一定要比正态或T分布要更肥尾）。