关于峰度和偏度的问题求指导

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各位好，最近闲下来在看一些关于定价和风险控制的书籍，自己觉得有些不明白想请教下各位。第一点是在对金融产品定价上有没有相关的论文比较针对性介绍三阶矩在定价中的作用的，希望有大神能推荐一些。感觉之前都主要考虑一阶矩和二阶矩，似乎有些欠缺（也可能是楼主看的书太老了，囧）。
第二点是比较一下市场收益率和偏度貌似个人感觉所谓牛市或者熊市，与偏度小于0或大于0是不是存在一个对应。这样的理解不知道对不对，还是只是个人的幻觉？
谢谢各位大神指导啦。。

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关键词：求指导 论文比较 风险控制 金融产品 不明白 指导

Very good question.

The most important reason is that for most commonly used distributions, almost none of them need to be determined by higher moments such as kurtosis or skewness. Even though for some asymmetric distribution or fat tail distribution such as exponential or t. They don't need these moments. So you don't need to model them. Of course, there is some exception such Cornish Fisher method for VaR calculation directly uses the 3 and 4 th moment.

The second reason is that most of the models are build on Brownian motion or normal density. Normal distribution can be totally determined by the first two moments. To model the skewness and kurtosis, people do is to introduce the following: time varying volatility, jumping, CEV, Stochastic Volatility, correlation between volatility and asset prices...

In a bullish or bearish market, the distribution of the return may be skew. But perhaps this is only a special sample period of a normal distribution. In the long run, the return is normal.

best,

Chemist_MZ 发表于 2013-5-25 21:07
Very good question.

The most important reason is that for most commonly used distributions, almos ...

Thank u and grateful for ur answer.
I wonder if I make it right ——the trick for the first issue is that there is simply few technically-feasible model to incorporate 3 or 4th moment in pricing financial assets?
And for the second problem, I am actually quite into that guess and I hope it is worth researching.

Dr.JohnDoe 发表于 2013-5-25 21:57
Thank u and grateful for ur answer.
I wonder if I make it right ——the trick for the first issue ...

1. Yes, you can think in that way. There is a tradition in finance that new model should more or less have a connection with the old model such as black-scholes.  Otherwise, the model will not be very popular if you introduce a totally different one. The reason is because the people has studied this area for so many years and find the normal framework has many good properties and the appearance of these models are all very beautiful. If you put 3 or 4 moments in, you can imaging how ugly the model will be. Ugly model will never get its place.

The "correct" way is that: when you find the normal distribution not work, try to make some little improvement but not abandon normal and find other distributions. Normal is very good in most cases, you don't need to find a complicated model for a special time period or a special asset class. Actually, stochastic volatility models are very very flexible I think it is more flexible than just include more moments.


2. Actually I have not consider about this topic before, may be you can check some papers. I think most of the study focuses on the empirical part, such as use different type of volatiltiy models (e.g. GARCH) to fit the data to test the some skewness effects such as leverge effect (NGARCH). Personally，I do not recommend you to study this topic. The problem does not need to be modelled in that way. Of course, you can study it for personal interest.

Just some suggestions, good luck

best,

Chemist_MZ 发表于 2013-5-25 22:24
1. Yes, you can think in that way. There is a tradition in finance that new model should more or l ...

Thank u for your answer. And I benefit a lot from your advice.