请教(急）：有限个收益数据及其概率，如何模拟价格路径？

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关于美式期权定价中，路径模拟问题。
有３６５个股票历史收益率R(i)=S(i)/S(0) (i=1,2...365); （现在时刻为０，到期时刻为３６５天后，每一天都可能执行期权），且知道将来该３６５个收益的概率分别P(i) （sigmaP(i)=1）。
问题：
如何用这些条件，模拟１００００条股票价格路径？

我这么想的： 通过３６５个已知收益与概率数据，模拟收益与概率之间的关系，再通过这种关系随机生成收益路径，从而得到股票价格路径。但我不知道具体怎样施行。

非常感谢！

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关键词：期权定价中 Sigma 股票价格 gmap 非常感谢 股票价格 收益率 天都 我不知道 如何

You don't need history prices, but you need a discounting curve.

1) Simulate the price of S as what you do for European option (i.e., dS = rSdt + sigma*S*dX).
2) Using LONGSTAFF & SCHWARTZ REGRESSION to make adjustment for American options.

See Paul Wilmott on Quantitative Finance Ch 80 for details.

Personally I don't recommend to use MC for American option, esp when the dimension is low.
Maybe consider to use FD or tree instead?

By the way, if it's a call option on a stock with no dividend-paying, it won't early exercise.

Thanks a lot.
you do make sense about my question,however, what you refers is just model-based (such as BS-model) ,so you can use LS-MonteCarlo to generate the paths, not dependent on historical prices.
but, i am pricing american options  is model-free, only using the market prices. the paths simulation is required when using Longstaff method(2001),and this is the point i am encountering.
how can i get the simulation paths?

You are right.
My proposal is based on BS model.

I am thinking there is no pricing method which is model-free, as model is always needed to simplify future world (i.e., price movement in this case). Using historical prices to project future prices is a model assuming that the future will follow the historical pattern.
One thing you might notice is that arbitrage will exist too if you use historical prices to calculate option value.

Please freely make comment. :)

1. for BSmodel, it's easy to simulate many  prices paths, that's,we can  take random number.
2. but now, I have only 1000 historical prices, assuming the future prices follows the historical pattern, how can i produce 10000 paths? just using those 1000 data via the order "randsrc" in matlab?

I believe that there is a statistic technique called "re-sampling" doing similar thing.
I am not good at this area.

Maybe you can get start from googling "re-sampling"?