带新人，凡是金融数学相关问题都可以发这里，大家一起解答。

麻烦楼主解释下：GARCH 和ARCH 模型，我觉得书上讲得太过于简单。

以下是引用alexander523在2008-7-21 14:56:00的发言：

能否推荐下金融数学的书啊，我觉得随机微积分好困难啊，

https://bbs.pinggu.org/thread-338947-1-1.html

慢慢看，半年看得懂就可以了。

最好有点测敦伦的基础，然后看看概率论再开始看这本书

如果学的是高等数学，而不是数学分析的人，

看测度论和积分论，可就难了，

如果半解，去看概率论也难懂的啊

  如果确实没有分析基础的人，我觉得直接背诵少量随机的运算公式也就够用了

_t以下是引用panet在2008-7-21 18:55:00的发言：
麻烦楼主解释下：GARCH 和ARCH 模型，我觉得书上讲得太过于简单。

如果你想多了解garch 和 arch，我可以建议你看看 eagle的几篇paper， 或者hamilton的那本 time series。

其实这两个模型就是很简单的，关键看你用的合适不合适了， garch in finance 主要用来model volatility 的，你可以搜索下有很多这样的paper，现实中也用的比较多。 模型设计者的初衷就是来研究一些， uncorrelated time series X_t but (×_t⁾² not independent ，eg. some financial returns

当你用的时候你会遇到一些，如何求model系数的问题等等，可以看看相关论文就行了。计量经济学的很多书都有介绍的，如果你不是学数学的话，还是不要看hamilton的那本了，太多algebra

请教一下关于期权定价的问题：在B-S公式中，看涨期权的S(T)大于K(T)和看跌时S(T)小于K(T)的概率怎么算？或者说S(T)是什么分布？

另一个，有个可以在T也可以在T/2时执行的期权，S(T/2)大于a的概率和S(T)大于b的概率一样么。我原来是学别的专业的，但愿我说清楚了。。。

拜谢答复！

请问美国金融数学phd一般需要什么样的背景才容易得到offer？

谢谢

generally olympic winner in math

few of such programms in even USA

以下是引用juedistar在2008-7-22 10:47:00的发言：

请教一下关于期权定价的问题：在B-S公式中，看涨期权的S(T)大于K(T)和看跌时S(T)小于K(T)的概率怎么算？或者说S(T)是什么分布？

另一个，有个可以在T也可以在T/2时执行的期权，S(T/2)大于a的概率和S(T)大于b的概率一样么。我原来是学别的专业的，但愿我说清楚了。。。

拜谢答复！

continues的情况下，ST=St*exp(mu-.5sigma^2+sigma*t^.5*z), where z follows Normal(0,1), this is from the GBM sde dS=S(mu*dt+sigma*dWt)

therefore Pr(ST>K) =Pr(St*exp(mu-.5sigma^2+sigma*t^.5*z>K)     (1), 

make z in one side in the inequality and use standard nor cdf to find the value of probability.

Actually log diff of St follows normal, in other word St-St-1 follows lognormal distribution

As to the second one,  you can calculate them by (1). and because the increment of Wt is independent, i.e. WT/2 and WT is indep since W0=0, therefore you can also find the P( A,B)= P(A)P(B)

 If you mean not specify the T/2 and T be the only two stopping times, I can show you a formula for stopping time t = inf(t: Wt=a or Wt=-b),   denotes Ta if Wt Wiener process touch a, and T-b for hitting -b. where a and b are positive real numbers.

Besides we know that E(Wt)=0, Then  Pr (Ta<T-b), standing for the wiener process first touch a not b.  by def of prob,

we have P(Ta<T-b) + P (Ta<T-b) =1,

and by means of Expectation, we have      a*P+b*(1-P)=0, we can get P.

PS: in your situation St will hit a and b, rather Wt. So you need to do little algebra to find proper a and b for Wt.

I hope this is clear for you.

以下是引用hoopmat在2008-7-22 13:47:00的发言：

请问美国金融数学phd一般需要什么样的背景才容易得到offer？

谢谢

you can try, that's all. Nothing is impossible.  As far as I know,  Berkeley, NYU, Princeton, Stardford, CMU, Clumbia are top tier university.  I also want to transfer to Clumbia which is the easiest one I can apply for a phd among those universities.

They will not require a lot of math knowledge but strong recommendation from some giants in Quantitative finance area, but the world best fm program is hold in France!

As a backup, you can also apply some phd degree in Probability, which is easier for you to come to US, then you can consider transfer to these tops.

Good luck!

以下是引用zzrays在2008-7-22 23:20:00的发言：

you can try, that's all. Nothing is impossible.  As far as I know,  Berkeley, NYU, Princeton, Stardford, CMU, Clumbia are top tier university.  I also want to transfer to Clumbia which is the easiest one I can apply for a phd among those universities.

They will not require a lot of math knowledge but strong recommendation from some giants in Quantitative finance area, but the world best fm program is hold in France!

As a backup, you can also apply some phd degree in Probability, which is easier for you to come to US, then you can consider transfer to these tops.

Good luck!

a little bit funny story you told

the guy asked you which kind of persons can enter PhD programm in financial mathemaitcs.

you answered that it is unnecessary for a mathematical guy.

 a little bit funny,

 also, the schools you mentioned above,  few of them have PhD program in financial mathematics.