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[金工金数] 如何确定最优garch模型参数

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franklin_lalala 发表于 2013-12-2 22:58:33 | 显示全部楼层 |阅读模式

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本帖最后由 franklin_lalala 于 2013-12-2 23:13 编辑

garch模型多用garch(1,1),我好想记得有个什么检验,来确定garch(p,q)中的最优的p和q,是什么检验来着……?. 1point3acres.com/bbs
是不是类似aic/bic的东西???……?
 楼主| franklin_lalala 发表于 2013-12-2 23:14:10 | 显示全部楼层
然后让bic最小的那个p和q?……?
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Exort 发表于 2013-12-3 00:55:39 | 显示全部楼层
意义不是很大吧。。基本没见过系统阐述这个问题的。。Paul Wilmott那堆砖头里倒是有一段话。。 (Chapter 51.8/P860)
Choosing the model means choosing the functional forms for p and q, or rather p − λq and q. This is not easy, principally because σ is not observable, so how can you model it? Strictly speaking, you ought to try and get p and q by looking at the statistics of the stock price S. Models such as ARCH, GARCH, REGARCH, mentioned below, try to do this. Then you would estimate λ from option prices, since λ is associated with how people value volatility risk, and that isn’t observable in the stock price series.
None of that is easy. So what seems to be more common these days, although harder to justify than the statistical approach, is choosing p − λq and q so that the model correctly prices exchange-traded options. Often this means picking a model that is tractable, has closed- form formulae for vanillas, and has sufficient degrees of freedom (in terms of parameters) so that those vanillas can be priced exactly the same as the market. I’m not going to go into the details of calibration, you should look in the Further Reading section for pointers in that direction. Instead I will first explain what is meant by a model, and then mention a few of the popular ones.
Focus on the volatility of volatility function q first. This governs how much randomness there is in the volatility model. Suppose volatility is low. Would you expect changes in volatility to be small or large? If volatility is around 5%, will changes in that level be ball park 0.05% per day or 2% per day? (I’m not expecting you to give me an answer. Bear with me for a moment longer.) And if volatility is about 30%, will daily changes be 0.05% or 2%? The question is about how does q vary with the level of σ? Most people answer that the higher the value of volatility then the bigger the daily fluctuations in it. This seems reasonable and is borne out by research. But it is far from being sufficient information to pin down the functional form for q. It may be an increasing function of σ, but which increasing function?
The same applies to the drift function p. Most people would say that volatility is mean reverting, and this should be reflected in p. But again this means little more than p is negative when σ is large and positive when σ is small. More information is needed.
To model volatility as a stochastic process you need some statistics, or a simple model that you can calibrate. Some further ideas on the statistical approach are given in Chapter 53. Now let’s look at the famous models.
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Exort 发表于 2013-12-3 00:56:15 | 显示全部楼层
本帖最后由 Exort 于 2013-12-3 01:05 编辑
. 1point3acres.com/bbs
觉得本身GARCH模型设定就是偏理论化的,实证上一点都不好用。。pq二阶时候参数限制就无比复杂了。。所以大家也不太纠结究竟pq取多少的问题,基本上只见过(1,1)(1,2)和(2,1)的。。理解得不是特别透彻。。随便说两句抛砖引玉下。。. visit 1point3acres.com for more.
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bigdrogon 发表于 2013-12-3 04:34:54 | 显示全部楼层
可以看EACH(data)结果的pattern
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 楼主| franklin_lalala 发表于 2013-12-3 21:37:09 | 显示全部楼层
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 楼主| franklin_lalala 发表于 2013-12-3 21:37:28 | 显示全部楼层
bigdrogon 发表于 2013-12-3 04:34
可以看EACH(data)结果的pattern

你看上面的结果~~
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Exort 发表于 2013-12-4 09:58:38 | 显示全部楼层
本帖最后由 Exort 于 2013-12-4 10:04 编辑
. 1point 3acres 璁哄潧
翻了一下文献好像确实都是用AIC/SC/MLE判断的。。
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