b**********5
发帖数: 51 | 1 Is Geometric Brownian Motion a Lognormal Random Walk? If so, why it's
lognormal, I
mean how could we know it's lognormal?
What are the usually used stochastic process with Lognormal Random Walk?
Finally what Geometric mean in the term Geometric Brownian Motion?
Thanks for idea in advance. |
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i**w
发帖数: 71 | 2 有同学提到了implied distribution，非常有道理.
首先简单的lognormal或者normal是不够用的，书上也都提到过为什么不够用，最直接
的就是volatility smile。可以加上些东西，比方说stochastic vol, 或者jump。或者
其他很丑的东西，比如一个简单的cut off,或者分段(把lognormal和normal mix在一块
儿)，这样就可以解决价格是付的问题。(丑不要紧，能用就行)
接着就是去fit market了，简单地说就是拿你觉得重要的market price(各种ATM price
或者其他的)作为target,fit出来model里的参数。其实就是去approximate market
implied distribution. 因为这个distribution肯定是奇奇怪怪，不是什么简单的解析
的函数，所以从另一方面也justify了上面模型的奇奇怪怪。
总而言之，normal/lognormal都是实际上用的模型的building block,所以还是要稍微
懂一些的。但是因为lognormal本身的一些好的性质，它作... 阅读全帖 |
|
i**w
发帖数: 71 | 3 有同学提到了implied distribution，非常有道理.
首先简单的lognormal或者normal是不够用的，书上也都提到过为什么不够用，最直接
的就是volatility smile。可以加上些东西，比方说stochastic vol, 或者jump。或者
其他很丑的东西，比如一个简单的cut off,或者分段(把lognormal和normal mix在一块
儿)，这样就可以解决价格是付的问题。(丑不要紧，能用就行)
接着就是去fit market了，简单地说就是拿你觉得重要的market price(各种ATM price
或者其他的)作为target,fit出来model里的参数。其实就是去approximate market
implied distribution. 因为这个distribution肯定是奇奇怪怪，不是什么简单的解析
的函数，所以从另一方面也justify了上面模型的奇奇怪怪。
总而言之，normal/lognormal都是实际上用的模型的building block,所以还是要稍微
懂一些的。但是因为lognormal本身的一些好的性质，它作... 阅读全帖 |
|
f*****s
发帖数: 141 | 4 Lognormal的定义：log(X) is normal, then X is lognormal.
GBM is a lognormal with log(X_t) ~ N(logX_0+(mu-sigma^2/2)t, sigma^2*t) |
|
j********9
发帖数: 162 | 5 I have some questions here:
Does the copula of M.R.V. LogNormal Distribution follow M.R.V. Normal
Distribution?
If yes, what is the covariance matrix of the copula distribution, is that
the normalized characteristic matrix of LogNormal Distribution?
What happen to the copula for T distribution (except Cauchy distribution) or
any elliptical distribution?
Can anyone recommend me some reference, online or book. I really want to
make it clear. Thank you so much. |
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A*****s
发帖数: 13748 | 6 到底啥样是normal model啊？
dS = u dt + vol dW?
normal model会造成负数的价格。。。至少比起lognormal来说完全不valid吧。。。
lognormal的challenge也就是在fitting的层面上
normal的challenge都在本质特性上的inconsistency了 |
|
A*****s
发帖数: 13748 | 7 到底啥样是normal model啊？
dS = u dt + vol dW?
normal model会造成负数的价格。。。至少比起lognormal来说完全不valid吧。。。
lognormal的challenge也就是在fitting的层面上
normal的challenge都在本质特性上的inconsistency了 |
|
k*****y
发帖数: 744 | 8 书上说把normal近似看成lognormal with volatity \sigma/S，lognormal就会小点。
怎么理解？ |
|
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I***l
发帖数: 19 | 9 请问哪位大牛有下面这片文章？能不能发一个电子版给我？万分感谢！
S. Schwartz and Y. Yeh, “On the distribution function and moments of
power sums with lognormal components,” Bell Syst. Tech. J., vol. 61,
pp. 1441–1462, 1982. |
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p*******p
发帖数: 13670 | 10 它的平均值很直接,如何证明一个lognormal分布的变量x的
variance=exp(a^2)*(exp(a^2)-1)呢? a^2是ln(x)的variance |
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i********y
发帖数: 346 | 11 My understanding is that the implied vol depends on the market strike price
distribution and the relationship between them can be shown following some
models such as BS. If the market spot price distribution happened to be the same
as Lognormal, then implied vol would not depend on strike price. |
|
k*****y
发帖数: 744 | 12 Q2.18 Suppose we price a digital call in both normal and lognormal models in
such a way that the price of call option with the same strike is invariant.
How will the prices differ?
the price of call option with the same strike is invariant是什么意思？
解答也没看懂，哪位来稍微解释一下？谢谢~ |
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i**w
发帖数: 71 | 13 不少时候quote price会用normal vol.
而且model interest rate的时候，会用到normal model的变种。
lognormal model也不能说valid...哪个model fit的比较好就用哪个呗 |
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a**n
发帖数: 3801 | 14 normal和lognormal不可能是equivalent measure啊 |
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A*****s
发帖数: 13748 | 15 肯定不是
别这么严谨，不然这本书能把你搞跳楼的
就当在同一个RN measure下假设一个lognormal一个normal
normal那个是不是discount martingale就别管了
但是这样做出来的price基本扯淡 |
|
k*****y
发帖数: 744 | 16 Q2.18 Suppose we price a digital call in both normal and lognormal models in
such a way that the price of call option with the same strike is invariant.
How will the prices differ?
the price of call option with the same strike is invariant是什么意思？
解答也没看懂，哪位来稍微解释一下？谢谢~ |
|
i**w
发帖数: 71 | 17 不少时候quote price会用normal vol.
而且model interest rate的时候，会用到normal model的变种。
lognormal model也不能说valid...哪个model fit的比较好就用哪个呗 |
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a**n
发帖数: 3801 | 18 normal和lognormal不可能是equivalent measure啊 |
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A*****s
发帖数: 13748 | 19 肯定不是
别这么严谨，不然这本书能把你搞跳楼的
就当在同一个RN measure下假设一个lognormal一个normal
normal那个是不是discount martingale就别管了
但是这样做出来的price基本扯淡 |
|
w******i
发帖数: 503 | 20 what is the answer?
my feeling is that lognormal digital call is less expensive than that in
normal model. |
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j*****l
发帖数: 73 | 21 想生成correlated multivariate lognormal distribution，因变量间的相关系数为0.
5，如何实现？
R中有个package“compositions”中有rlnorm.rplus()函数可生成多元对数正态分布，
但不能控制相关系数，不知哪位高手能帮忙生成出来，3个包子奉上。 |
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b***y
发帖数: 14281 | 22 既然有人争论方的学术水平，就上网搜了一下。应该说这个水平对于一个junior
faculty来说可以算是很牛B了，但是对于老方这种senior的已经搞了一辈子的人来说，
就只能算so so。不要说是院士，离aps fellow的级别也还差了不少。引用率最高的一
篇文章还是95年到了arizona之后跟老外合作的，被引118次，这也是方唯一一篇被引用
上百次的文章。可见方励之89之前确实没有做出过什么重要的工作，他的名声和地位绝
对是靠政治得来的，当然其中部分的也是80年在中国搞科普所得，必须承认科普工作也是
有重要的社会意义的。
(BTW，有人说你这个搜索未必完整。不错，确实不能保证100％毫无遗漏。但是我
用的search engine is THE search engine everybody in this community uses today.
So, if any article is not found by this search engine, sadly, it simply doesn't matter,
because no one would ever n... 阅读全帖 |
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s*******h
发帖数: 1361 | 23 Asian option的underlying是average price, 用moment matching是为了把sum of
lognormal变成lognormal.UWTI实际上是三倍的SPGSCLP index, roll是5天contract
cap weighted,一天roughly switch 20% capital (我说roughtly是因为里面有time
lag和normalizing constant,有兴趣看下SP的methodology).Index的算法是average of
return,也就是说rolling window中return变成sum of normal,不需要moment match已
经是normal distribution, 算下basket sigma就可以了，都是analytic form.
一句话说，Asian option本质是average of price（lognormal）算的是return of
average, UWTI rolling本质是average of return(normal). |
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f********k
发帖数: 136 | 24 申请的是MSc in Mathematical and Computational Finance，我知道版上还有同学想申请他们家的，所以我凭记忆列了一下我被问到的问题，供作参考。
1. What's the definition of continuity of a f(x) at x0. Given some examples,
tell if they are continous or not。（有个例子是某个函数在有理数上为0，在无
理数上为1，问连不连续，猜了连续，其实不清楚，不知道对错)
2. Matrix, eigenvalue and eigenvectors related questions. How to find limit
(1/c^n)*A^n, when n getting to infinity, if A is a symmetric matrix and the
limit exists. (这题跟他们网上的admission exercise某一题一模一样，主要就是证
明原对称矩阵跟特征值对角矩阵相似，原问题转化为对角矩阵的问题。）
3.Some ... 阅读全帖 |
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h******i
发帖数: 661 | 25 你们学校ap能发这么多paper?
1989
Cosmological implications of quasar-galaxy associations, L.Z.Fang, Y.Q.Chu
and X.F. Zhu, Mod. Phys. Lett., 4, 887.
Geometrical optics in an inhomogeneous universe, L.Z.Fang and X.P.Wu,
Chinese Phys. Lett., 6, 233.
Quasar clustering and its cosmological implication, L.Z.Fang, Inter. J. Mod.
Phys. A4, 3477.
L'Osservatorio astronomico di Pechino: la sua storia, il presente, L.Z.Fang,
Scienza e Tecnica, Annuario della EST 88/89 404.
Overview on the frontier of high energy astr... 阅读全帖 |
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b***y
发帖数: 14281 | 26 No. The search include his early works up to 1978. Here is the same list
sorted by year.
1) The Influence of Gravitation on the Vacuum State.
By Li-Zhi Fang.
Acta Phys. Sinica 27 ( 1978) 181-18.
2) THE STRUCTURE AND STABILITY OF THE ABNORMAL NEUTRON STAR.
By Li-Zhi Fang, Qin-Yue Qu, Zhen-Ru Wang, Tan Lu, Liao-Fu Luo.
Sci.Sin.22:187-198,1979.
3) Some Recent Developments in Astrophysics. (Talk).
By Li-Zhi Fang, A. Qadir, R. Ruffini.
In *Nathiagali 1980, Proceedings, Physics and Contemporary Needs... 阅读全帖 |
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S******8
发帖数: 24594 | 27 老方到美国后发的文章列表，你自己看吧：
1990
174. Biased clustering in a universe with hot dark matter and a cosmic
string, L.Z.Fang, S.P.Xiang and L.Yan, Astr. & Astrophys. 233, 1.
175. Periodicity of redshift distribution in a T-3 universe, L.Z.Fang, Astr.
& Astrophys. 239, 24.
176. An upper limit to quasar's peculiar velocity, L.Z.Fang, Y.Q.Chu, X.F.
Zhu and L.F. Wang, Inter. J. Mod. Phys., 5, 2993.
177. Quasar pair and quasar's peculiar velocity, L.Z.Fang, Developments in
general relativity, astrophysics and qu... 阅读全帖 |
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x**********t
发帖数: 45 | 28 遇到一个问题，大家帮我看看我想得对不对？
generate random number from a distribution which is skew to left.
假设生成了500个数据，Y_{500}.
现在我在每个数据上都乘上一个positive number,这些positive values都是从
lognormal distribution中生成的。但是 每一个数据是从不同的lognormal dist生成
的（mean和SD都不同）。 用X_{500}表示。
那么Y_500 * X_500有可能skew to left,也有可能skew to right.是不是这样？
谢谢了。 |
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r*****t
发帖数: 286 | 29 ☆─────────────────────────────────────☆
lognormal (lognormal) 于 (Thu Feb 8 00:19:49 2007) 提到:
我所在的学校曾经排在“最不用功的大学”排行榜的top10
我的专业倒是“热门”专业--物理
有C++，MATLAB，Excel/VBA经验
曾经用Monte Carlo和finite difference做过numerical simulation.
现在主要是simulate 一些 Chaotic dynamics
准备今年夏天毕业, 两个星期前开始在monster, hotjobs上post了简历,基本没人理.
现在挺困惑,是不是烂校的phd,就算是物理,也根本就没指望? 我也不想shoot high, 只
是想入个门而已, 找个小点的hedge fund, 只要能给办H1就行, 是不是这样也很难?
简历post了两周，也没有headhunter找上门，我是不是应该主动去联系他们？
像我现在这种情况, 是不是只有读名校mfe才是唯一的出路?
希望各位大侠指点迷津，多谢！Bow~~~
☆ |
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a**x
发帖数: 9 | 30 Does BGM model assume forward rates follow lognormal distribution? I am
modeling a 25-year option. Interest rates from lognormal distution can
exceed 200% for a 25-year projection. That is why I gave up on BGM model and
hoping CIR(extended version) can get more reasonable returns. Now I
modified my model as follows: dSt/St=(R(t)-sigma^2)*dt+sigma*Rho*dWt, where
R(t) is the output from extended CIR, instead of current yield curve. Do you
think this approach is doable?
Another problem is the opti |
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r**u
发帖数: 69 | 31
i'm assuming these 2 assets are stocks with lognormal distributions.
K
this is a spread option. don't think there is closed formation solution.
this is not too hard as S1*S2 is lognormal itself. this is standard black-
scholes. |
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t*******z
发帖数: 606 | 32 basically you are talking about cross greeks. pretty tricky.
the common practice on interest rate desk is:
if it is normal model, then cross greek between vol and delta will be small
and you don't need to worry too much.
if it is lognormal model, vol will change when rate change, lambda( or cross
) will be significant.
That's the major reason why most interest rate desk use normal model instead
of lognormal model. |
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f********k
发帖数: 136 | 33 第一个的确是没印象了，太久远了。
lognormal的mgf的确对所有t>0都无界，但是在t<=0的情况下有界[0,1]，因为e^tx只能
在[0,1]之间（x>0 because of lognormal)，因此它的期望值也只能在[0,1]之间。题
目是让你“say something about it"。 |
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a*****r
发帖数: 1539 | 34 以前的说法是,rate低的话,比较偏向于normal,rate高,比较偏向于lognormal,可是这两
年的rate很低,真的看swaption vol的skew,也不是normal的.现在不都用CEV或者
shifted-lognormal model了吗? |
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i***k
发帖数: 4 | 35 lognormal does not have strictly positive density on R.
could be lognormals with different parameters, but with the same underlying
normal random variable W. |
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x**********t
发帖数: 45 | 36 遇到一个问题，大家帮我看看我想得对不对？
generate random number from a distribution which is skew to left.
假设生成了500个数据，Y_{500}.
现在我在每个数据上都乘上一个positive number,这些positive values都是从
lognormal distribution中生成的。但是 每一个数据是从不同的lognormal dist生成
的（mean和SD都不同）。 用X_{500}表示。
那么Y_500 * X_500有可能skew to left,也有可能skew to right.是不是这样？
谢谢了。 |
|
n**f
发帖数: 121 | 37 I am having great trouble with using Maximum Likelihood to estimate
distribution parameters. I will appreciate if anyone can help me find out
what went wrong.
Assume that I have M iid samples of random vector V, denoted by v_1,v_2,...v
_M. Define random variable X = f(V|theta) where f is function whose closed
form is known but parameter theta is unknown.
I assume X=f(V|theta) follows a lognormal distribution logN(mu,sigma) where
mu and sigma are unknown. My purpose is to JOINTLY estimate theta, ... 阅读全帖 |
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f*******l
发帖数: 828 | 38 我用 genmod fit一个数据，看起来response variable的分布可以是lognormal也可能
是gamma... 然后我用link=log dist=normal算出来的结果比link=log, dist=gamma的
AIC/BIC大，这样是不是一定就要用link=log dist=gamma了.
可是我觉得link=log dist=normal不是更能说明lognormal么（或者我理解错了？），
然后gamma的canonical link不是应该是 1/ ?
我特别希望能用link=log dist=normal算出来的结果，但是因为BIC大一些，所以不知
道怎么写report... 是不是有别的方法来看genmod下那种方法更好呢？ |
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y*****w
发帖数: 1350 | 39 各位distribution大拿好，我最近有个sample size calculation project。是count
data，具体说是number of patient visits, with number of episodes for each
number of visit。请各位帮着参谋看一下我做的是否合适，给些意见。
Sample data如下：
# patient visit episode
---------------------------------
1 156
2 287
3 589
4 899
5 1535
6 1408
7 1017
8 ... 阅读全帖 |
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y*****w
发帖数: 1350 | 40 Because as I mentioned, SAS PROC POWER with the TWOSAMPLEWILCOXON statement
, which I used for the sample size calculation, has no NEGB option.
Actually I found I don't need PROC GENMOD in this context, because I found
that lognormal distribution better fits my data than Gamma distribution,
whereas PROC GENMOD does not have the lognormal option as a distribution. I
found the following SAS example using PROC UNIVARIATE very useful in that it
provides simple and straightforward statistics and gra... 阅读全帖 |
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x*******u
发帖数: 500 | 41 有个数据， value较低的时候差不多是lognormal distribution， 但是会有几个很高
很高的value。 比如说在0-7200 是lognormal， 然后在17000， 和30000各出现一次。
我想算出出现下一个超过15000的probability， 请问应该怎么做。
谢谢 |
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m****a
发帖数: 604 | 42 技术上讲是没错的。收入是lognormal分布，属于偏态分布。50%的人收入低于平均值。对于经济分析，如果在乎经济总量，那么用平均值多点。如果是个体收入，那么用中值多点。 |
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s******r
发帖数: 5309 | 43 收入分布函数是lognormal，取对数满足正态分布。用几何品均值代替算数品均值会好
点。 |
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l******n
发帖数: 9344 | 44 Detection of two-component mixtures of lognormal distributions in grouped,
doubly truncated data: Analysis of red blood cell volume distribution
1991
C.E. Mclaren, M. Wagstaff
to f********[email protected]
baozi
thanks |
|
l*******g
发帖数: 393 | 45 我辛苦很久的一篇single author的paper昨天被review回来了，结论是minor revision
，呵呵
不过，明摆着Referee是个非常牛的人，看出一个问题，就是说
能不能找到一个已知的广泛应用的概率分布，这个分布在计算多元分布函数（cdf）比
较快，而计算其gradient比较费功夫。如果这样，我的算法就特别有意义了，呵呵，不
假设多元函数component之间independent
我现在能想到的是多元lognormal，还有其他吗？谢谢，多多益善 |
|
m********0
发帖数: 2717 | 46 对于Expected Return,
它是怎么算的，基于lognormal 分布+historical还是implied volatility?
他里面有个选项限定underlying变化范围，我怀疑它到底用没用什么分布。 |
|
m****a
发帖数: 240 | 47 TA 无所不能。
把我的account value 做 TA 分析甚至比大盘指数TA分析还准。
我的帐户跌多了要涨，涨多了要跌。
当然曲线也符合 lognormal distribution with 50% expected yearly return and 30
%
volatility. |
|
m********0
发帖数: 2717 | 48 RSI
= 100-100/(1+RS)
= 100* RS/(1+RS)
= 50 * [1-(1-RS)/(1+RS)]
= 50 * [1-(-)/(+)]
RSI low => >> =>
P( < in the following observation | >> in the past)
is big => P(Return = *n + *n > 0) is big
Assumptions are:
normal dist of ROC, or lognormal dist of Ret,
observation time is enough
>> means strong trend,
so you are using RSI as counter-trend indicator
TA is more or less empirical semi-scientific statistical approach.
All just mapping some data int... 阅读全帖 |
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m********0
发帖数: 2717 | 49 The thing is the it's not a graph for any stock. I just make it with the
following R code,
require(TTR)
ret<-cumsum(rnorm(252,sd=0.036))
ret2<-exp(ret)
p<-50*ret2
ma20<-SMA(p,20)
ema20<-emaTA(p,20)
ema50<-emaTA(p,50)
plot(p, type="l")
lines(ema20, type="l",col='green')
lines(ema50, type="l",col='red')
and I used lognormal distribution for the returns, textbook assumptions
for
a big group of models.
skeptic(as exists everywhere), yes, I borrowed this idea from ET. Please
don
't rush to criticize,... 阅读全帖 |
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