关于crr(二叉树)期权定价模型什么时候概率p为负值？

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crr (二叉树) 期权定价模型在使用的时候必须求参数p,u,d，在crr模型里计算p,u,d的公式为：p=(exp(r*Δt)-exp(-σ*sqrt(Δt)))/(exp(σ*sqrt(Δt))-exp(-σ*sqrt(Δt)))，u=exp(σ*sqrt(Δt))，d=exp(-σ*sqrt(Δt))，其中r为无风险利率,σ为股票价格波动率,Δt为单步时间步长,我想问的是什么时候概率p为负值？有对这方面感兴趣的请多加讨论非常感谢。

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关键词：期权定价模型 定价模型 期权定价 CRR 二叉树 期权 概率 负值 二叉树 CRR

probability不能为负吧

shalou1 发表于 2010-4-21 10:34
crr (二叉树) 期权定价模型在使用的时候必须求参数p,u,d，在crr模型里计算p,u,d的公式为：p=(exp(r*Δt)-exp(-σ*sqrt(Δt)))/(exp(σ*sqrt(Δt))-exp(-σ*sqrt(Δt)))，u=exp(σ*sqrt(Δt))，d=exp(-σ*sqrt(Δt))，其中r为无风险利率,σ为股票价格波动率,Δt为单步时间步长,我想问的是什么时候概率p为负值？有对这方面感兴趣的请多加讨论非常感谢。

it should not be negative.

CRR tree can produce negative probability, this is known for more than 15 years

irvingy 发表于 2010-4-22 04:36
CRR tree can produce negative probability, this is known for more than 15 years

how to explain?

Enthuse 发表于 2010-4-25 07:31
how to explain?

I don't like you, so go figure yourself

二叉树模型中P的计算过程告诉我们，该模型是建立在某一随机试验即符合二项分布又符合正态分布的基础上，而正态分布中各个参数已知，二项分布中各个参数是依据正态分布参数计算。同时模型具有假设条件U*D=1,最后得出二项分布中各个参数的结果。在P 的表达式中，我们可以看到，u-d>0，当a<d时，p就小于零。其中a只和无风险利率以及时间间隔相关，所以当正态分布中方差较大时，p就小于0。
以上仅仅是从模型计算过程方面对p小于0的解释，即当某种证券的波动率较大且当时的无风险利率较大时，其依据二叉树模型概率p将小于零，我们在这里看到当p小于0,1-p就将大于1！所以在我看来，之所以会出现p<0的结果，关键在于正态分布的基础性假设以及U*D=1的假设！即当a-d<0时，该种证券不符合二项分布，产生的原因可能与时间间隔太大，等因素相关！而从另一个角度该概率属于无风险概率即不同于随机分布概率，从无风险概率的推导过程我们可以看到，该负值概率与个体对未来预期即无风险收益率相关！

irvingy 发表于 2010-4-25 08:05

Enthuse 发表于 2010-4-25 07:31
how to explain?

I don't like you, so go figure yourself

you have shown you arrogance in public.
u have successfully made yourself a laughable stooge in this forum.

Enthuse 发表于 2010-4-26 05:04
you have shown you arrogance in public.
u have successfully made yourself a laughable stooge in this forum.

well, here're the reasons why I don't like you
first, you're a charlatan, ignorant of the well-known fact, you make the claim "it should not be negative"
second, you're lazy, the answer to your question is just a google search away, but you asked me to explain
third, you're rude, even my boss uses phrases like "could you please..." and "thank you" when he asks me to do something
fourth, you want everybody to love you, otherwise you just call him a stooge, don't you
how pathetic you are

irvingy 发表于 2010-4-26 08:04

Enthuse 发表于 2010-4-26 05:04
you have shown you arrogance in public.
u have successfully made yourself a laughable stooge in this forum.

well, here're the reasons why I don't like you
first, you're a charlatan, ignorant of the well-known fact, you make the claim "it should not be negative"
second, you're lazy, the answer to your question is just a google search away, but you asked me to explain
third, you're rude, even my boss uses phrases like "could you please..." and "thank you" when he asks me to do something
fourth, you want everybody to love you, otherwise you just call him a stooge, don't you
how pathetic you are

a post from a stooge like you is worth nobody's time to answer. but i will make an exception this time.

first of all,  judging anybody is way beyond your small mind and limitations.  
second, this is a forum to discuss anything. ranging from the simplest facts to the deepest insights.  calling anyone lazy can only
be a self-refelction of caller himself. you revealed your rudeness and arrogance here, and it hinders you from seeing the
scope of any topic, including this one.

third. it is laughable that a stooge as rude as you are  is calling others rude. it seems your boss is an extra nice person.
usually people would not be so nice to som nitwit like you who could read rudenss from three words "how to explain"
and took offense so easiy and quickly.

fourth, i can tell you for sure. love from a rude and arrogant person like you is lack of taste and narrow-minded
at best and certainly not a pursuit of any decent human beings. before you rush to call others pathetic,
go get a life yourself.