a***r
发帖数: 420 | 1 弱弱地问一个关于EM algorithm的基础问题，
大家都知道：(theta 为新一轮估计值，theta’为上一轮估计值)
L(theta) = Q(theta, theta')- H(theta,theta')
where H(theta，theta')=E(log[f(x|y,theta)]|y,theta')
为啥H(theta,theta’)总是小于等于H(theta',theta') 呢？
书上简单说了下，by Jensen‘s Inequality，
但是愚鲁的我没有想明白。。。
望版上大虾指点！ |
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n*****n
发帖数: 3123 | 2 E(-log[f(x|y,theta)/f(x|y,theta')]|y,theta')>=-log[E(f(x|y,theta)/f(x|y,
theta')|y,theta')] by jensen's
the right hand side is 0 after integral since the expectation is w.r.t
f(x|y,
theta')
baozi please |
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s******e
发帖数: 1751 | 3 my 2 cents:
there are two parts of theta
theta F is the time value of option. this theta is negative, coz time value
always diminishes as the option approaches expiry.
theta F is the financing of option, aka discount factor of future cash flow.
If your option is deep in the money, then it approaches to expiration, you
are closer to receiving a positive cashflow. so this theta is positive.
theta = theta T + theta F |
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a**m
发帖数: 102 | 4 【 以下文字转载自 Quant 讨论区 】
发信人: attm (zhenqi), 信区: Quant
标 题: 关于希腊字母theta，急，在线等！
发信站: BBS 未名空间站 (Thu Dec 24 09:48:33 2009, 美东)
zhou xinfeng的书说（page 155）：deep-in-the-money put option with no dividends will have positive theta. That's also the reason why it can be
optimal to exercise a deep in-the-money American put before maturity.
后面一句没明白，既然theta是正的，option会升值，为什么要提前exercise？ |
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h*******r
发帖数: 1083 | 5 哪里有rienmann theta函数的公式表呢？就好像三角函数，有sin(a+b)=...这样的公式
，我想多知道一些关于riemann theta函数的。wiki上没找到，一些讲riemann面之类的
教科书上也没有。
我在研究中发现了一些theta函数恒等式。我不是专门搞这个的，如果想自己证明这些
恒等式，有难度。我想，应该先查一下公式表，可能套一下公式就成了。 |
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s*******s
发帖数: 1568 | 6 there is no contradiction. The theta is positive for euro put option, which
imply the option price will increase
when excise. the final excise of euro put option is equivalent to early
excise of america option. Thus it is
optimal to early excise the america option. theta of euro and american
option is different.
dividends will have positive theta.
That's also the reason why it can be |
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T******r
发帖数: 257 | 7 这是不确切的,正theta不是原因,真正根本原因是underlying的正drift.
正theta和optimal to exercise都是正drift(和put的payoff)的结果.
dividends will have positive theta. That's also the reason why it can be |
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n****e
发帖数: 629 | 8 以俺的浅见，认为是这个意思：
american put options的pdf是分段函数，在optimal exercising point处，c_{xx}是
不连续的。所以c_t在optimal exercising point也是不连续的。
common sense告诉我们，theta肯定得是负的；那么如果你得到正的theta，说明你的
pricing formula已经失效了。这个时候就是below optimal exercising point了。所
以要提前exercise。
dividends will have positive theta. That's also the reason why it can be |
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Q***5
发帖数: 994 | 9 From Crack's book, answer to 2.2:
"Option value decays toward kinked final payoff as expiration approaches.
This time decay is called theta. We usually think about theta as being
negative for plain vanilla options, but there are two clear exceptions. A
deep in-the-money European-style call can have positive theta if the
dividend yield is high enough--because high dividends can push price down
below intrinsic value and the option then has to 'decay upward' in value as
expiration approaches ...." |
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c****2
发帖数: 31 | 10 For Call option without dividend, theta < 0
For Call option with dividend, theta could be positive
For Put option, if it is deep in the money, theta > 0. In this case, early
exercise is preferred |
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g********g
发帖数: 65 | 11 我的理解 theta is Partial put value/ partial (T-t) ,随着时间的推移， 随着T-t 越来越
小的话，postive theta means put options value will decrease. |
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c****t
发帖数: 19049 | 12 Theta / Pure (4 to 8 Hz) / 30 Minutes / This is the region between sleep and
wakefulness, in which dreaming and other dream-like or hypnagogic
experiences occur. It's that bit just before you actually fall asleep at
night, or just before you are really awake in the morning. They say it's in
this band that the unconscious talks to the conscious mind. It also seems to
be connected with psychic or ESP-type functioning. Found in states of deep
relaxation, theta activity is also associated with burst... 阅读全帖 |
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h**********c
发帖数: 4120 | 13 asking function of theta
Baozi 2~5
for a function phi = f( theta)
so in two dimension, the points along a circle, points are compressed to x-
axis, but y is a pivot of splitting.
The nearer the point near the x-axis, the more compression.
Thought for days, no smooth solution.
Something like the Von Mises distro in Wiki.
Thanks |
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c********i
发帖数: 586 | 14 每次收到PHI THETA KAPPA邀请信都直接扔掉.
这个学期要毕业了,想了解一下参加这个PHI THETA KAPPA,对于毕业找工作以及以后上
学申请奖学金有什么好处吗? 谢谢. |
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l******o
发帖数: 298 | 15 theta能衰变出3个pai粒子，而tao能衰变出2个pai粒子。
theta和tao又是同一种粒子，怎么就能怀疑对称不守恒了。
比如说生产两个一样的炸弹，但是他们的爆炸结果不一样
很正常吧，也有很多随机因素在里面啊？对不对？ |
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B*********h
发帖数: 800 | 16 ☆─────────────────────────────────────☆
lachlan (啦可愣) 于 (Wed Jun 6 20:12:06 2007) 提到:
这个问题一般都是怎么解决的？
我们的theta p/l是在昨天的数据基础上加一天，其他变量都不变，然后算这个加了一
天和没加一天的差价；但是一到ex div date就给出巨大的theta p/l，因为那个股价的
drop没有算进去。这种情况下能不能把昨天的stock price减掉dividend，重新算p/l?
☆─────────────────────────────────────☆
Vishnu (Time Dealer) 于 (Wed Jun 6 20:15:21 2007) 提到:
No.
?
☆─────────────────────────────────────☆
lachlan (啦可愣) 于 (Wed Jun 6 21:15:05 2007) 提到:
what would you do?
☆─────────────────────────────── |
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a**m
发帖数: 102 | 17 zhou xinfeng的书说（page 155）：deep-in-the-money put option with no dividends will have positive theta. That's also the reason why it can be
optimal to exercise a deep in-the-money American put before maturity.
后面一句没明白，既然theta是正的，option会升值，为什么要提前exercise？ |
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Q***5
发帖数: 994 | 18 I see your point.
My reasoning was: suppose at some time t1
your assumption, the underline goes down, so at a later time t2>t1 (but t2
), c_t2
I guess we should not have used the example you gave: theta by definition
only considers the change of option price w.r.t time t, holding other
variables constant -- this includes holding stock price constant.
More specifically, let C(t,s_t) be the option price at time t with stock
price s_t. |
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p*****k
发帖数: 318 | 19 this might a tautology:
my understanding is that with high dividend, it drives the option
price below its intrinsic value when it's deep-in-the-money,
(one way to see this is that Delta does not approach 1 fast enough
due to the extra exponential factor)
so there the time-value of the option becomes negative. since the
time-value approaches zero closer to the expiration, Theta becomes
positive.
i think sometimes ppl are also interested in the so-called
"driftless theta" by ignoring the discount |
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p*****k
发帖数: 318 | 20 theta only reflects the time value of the option, one needs to
consider the other part: moneyness, i.e., either in the money (ITM), ATM or
OTM (in QL365's words, the option value also depends on s).
one interesting question is for (exotic) american options, whether
the early exercise region could be determined by some criteria on
theta. this seems generally not true, but i remember seeing some
paper using this as a good approximation. |
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a******6
发帖数: 78 | 21 john Hull那本书上提到了:
"option traders usually rebalance their portfolios at least once a day to
maintain delta neutrality. It is usually not feasible to maintain gamma and
vega neutrality on a regular basis. Typically a trader monitors these
measures. If they get too large , either corrective action is taken or
trading is curtailed."
为什么只提到了delta gamma and vega neutrality，而没有Theta呢？
还有一个问题：
assume BS and delta-neutral portfolio, then:
\theta + (1/2)\gamma S^2 \sigma^2 = r\Pi
where \Pi is the portfol |
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w******g
发帖数: 271 | 22 各位 ，一个有点弱的问题，
为什么in the money put option has positive theta?
既然已经是in the money，不是随着时间更容易变成ATM或者OTM吗，为什么theta反倒
可能是正的？
谢谢各位！ |
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W*******d
发帖数: 63 | 23 two forces:
1. negative theta decay
2. Time value change from excercise
if 2>1, the theta would be positive
considering a senario of very high interest, it is much better to exercise
now |
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h******d
发帖数: 4761 | 24 各位大侠一般爬有雪的山，穿Arc'Teryx Theta AR Jacket里面还要穿什么厚一点的衣
服吗？
今天试了觉得这衣服看起来好薄呀，保暖到底怎样呢？
可以穿来滑雪吗？
Arc'teryx Alpha SL Jacket跟Arc'Teryx Theta AR Jacket区别大吗？
谢谢回复。 |
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w****l
发帖数: 6122 | 25 对于买家来说，theta值要小于多少，才是比较有利的？ |
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m********i
发帖数: 298 | 26 Market decides the theta, buyer and seller on the same start line.
Neither side is advantageous.
Buyer return is positively skewed, while seller return is negatively skewed. |
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W******r
发帖数: 789 | 27 option的gamma和theta之间有一个trade-off。如果你买option，那么你有convexity的
优势，但是要go against time decay。如果你卖option，那么你有time decay的优势
，但是要go against convexity。似乎大部分option的书和网上的资料都是认为time
decay比convexity重要，主张以卖为主。但是我个人的经验却似乎不是这样。虽然卖
option有time decay的优势，但是因为go against convexity，一旦错了会输得很惨。
大家对此怎么看？ |
|
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r****e
发帖数: 9 | 29 find a Theta(nlgn) algrithm that given a set S of n integers and another
integer x, determines whether or not there exist two elements in S whose sum
is exactly x.
I thought it long time, but still no clue. Thanks a lot. |
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c********i
发帖数: 586 | 30 请问woshiYanZi, 你是F1还是其他身份?
我们这里community college非美国公民奖学金都没有机会申请.我上次想申请州里的
nursing scholarship,但是第一条就把我刷了,因为我是F-1,不是US citizen. 在CC的3
年里,问了不少,可就是没有一个我的身份可以申请的.
不过你说的PHI THETA KAPPA可以转,我倒是要去学校问问.要是我们这里也给转,那我就
去把申请交了. |
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G**********y
发帖数: 343 | 31 学长们，请问我今年5月份ADN毕业， 还有必要申请这个Phi Theta Kappa membership
嘛？申请这个也就主要是为了申请奖学金，这马上毕业了也没什么希望了吧。还是将来
上BSN还可以继续申请奖学金？
本来去年问这个结果没人理我，今年没发通知问要不要加入，就直接寄表格，PPT和介
绍了，这效率也太慢了吧。 |
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l******o
发帖数: 298 | 32 pion is pseudo-scalar.
(-1)(-1)(-1)(-1)=(-1)(-1)
如果theta能衰变出4个pai粒子，而tao能衰变出2个pai粒子。
就可以说对称了吗？ |
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s*********3
发帖数: 3 | 33 对于BS模型下,如何理解Europe call option的theta是负的(关于passage of time),
有没有人可以给一点intuitive的解释. 而后为什么put 可能是正的呢...
琢磨起来觉得复杂,觉得随着T变化,S_T变化的有点复杂.
再问: 如果此时刻是0时刻,T时刻到期,那么假设在t时刻股票变成了Se^(rt) 那么call
option价钱如何变化啊? |
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T******r
发帖数: 257 | 34 这是有payoff函数决定的.
通俗的说, T越长, call成为in the money的几率越大所以越值钱, 相对应就是
theta为负.
那你会问put为什么不是这样, 因为call的upper limit是无穷大. 而即便是deep in
the money的put也是有上线的, payoff=K when S=0. 所以一定情况下, 对于
put T越长反而不是越值钱.
你把BS公式写成forward的函数就可以知道你另一个问题的答案.
call |
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l*****i
发帖数: 3929 | 35 有可能得到更多的interest啊
dividends will have positive theta. That's also the reason why it can be |
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a**m
发帖数: 102 | 36 是有可能，但看书上这句话的意思是从theta是正的就可以推出该提前exercise了？ |
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a**m
发帖数: 102 | 37 但实际情况好像就是这样的，你可以算算该提前exercise的场合下，theta就是正的。 |
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l*****i
发帖数: 3929 | 38 但是是不是“只要theta>0就一定early exercise”? |
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a**m
发帖数: 102 | 39 怎么推出有可能的？或者说如果theta一直是负的（european call的情况），为什么能推
出（或者说怎么关联着）永远别提早exercise呢？ |
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d*j
发帖数: 13780 | 40 好像 deep in the money european call
theta 也可能是正的？
看看 heard on the street
是因为越到后来， optionality 越小， 对这个call越好
能推 |
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n****e
发帖数: 629 | 41 顺便问一句，zhou的书和joshi的/crack的比起来，有没有特长之处？考虑是不是买一
本……
dividends will have positive theta. That's also the reason why it can be |
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a**********2
发帖数: 355 | 42 that's not the reason//
他写的有歧义.
dividends will have positive theta. That's also the reason why it can be |
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Q***5
发帖数: 994 | 43 Perhaps the author means to say:
Large dividend push CURRENT call option value toward 0, but since the call
is deeply in money, at maturity, the option price (equals the intrinsic
value) should be positive, therefore, theta should be positive.
If so, I think ThatYear's explanation is right: it is just about option value converges to intrinsic as t-->T
Still, it seems that the author assumes that as dividend increase, the call option value decrease -- but the intrinsic value at T does not decreas |
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Q***5
发帖数: 994 | 44 In that case, the earlier the better -- i.e. theta is negative. |
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T*******t
发帖数: 9274 | 45 你搞清楚theta的定义了吗？
是dc/dt 还是dc/d(T-t)? |
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Q***5
发帖数: 994 | 46 My understanding is dc/dt.
Can you explain using the example you provided, why theta should be positive? |
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e****d
发帖数: 333 | 47 theta 没有 dividend 是negative的，是不是说option的价格就随时间减少？那越早
exercise 越好了？这是不是和不早exercise矛盾？还是因为两个说法的前提假设不同
？ |
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Q***5
发帖数: 994 | 48 But then, a reasonable buyer will realize this and will not buy it unless
it is priced below the value indicated by BS formula.
theta is the partial derivative of the option price with respect to time,
that is, it consider how the price change as time passes, holding other
factors constant. But in reality, other factors (especially the underline)
is NOT constant. By Ito's formula, you also need to add the term: 1/2*f_{ss}
(t,s)*sigma^2 dt, and you should end up with r fdt -- even there, we are |
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e****d
发帖数: 333 | 49 theta>0为甚要early exercise 呢？不是时间越长价值越高？这个怎么理解呢？谢谢了。 |
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l*******r
发帖数: 3799 | 50 theta represents the time premium. Of course it will drop as approaching to
the expiration day.
了。 |
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