b***k
发帖数: 2673 | 1 今天k书的时候想到的，
我们常说的用什么BS啊，这个模型那个方法给option pricing，
那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
如果是一回事，那有个问题我就不明白了，
不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
没有风险的，也就没有赚头可言了，那谁还会去买？
还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。 |
h**********y
发帖数: 41 | |
k*******d
发帖数: 1340 | 3 我的理解是，BS定价给出的是理论价格，实际市场的价格，如果在exchange交易的话，
还是由supply/demand决定的，只不过在理想的情况下应该和理论价格接近， |
D*****a
发帖数: 2847 | 4 are you kidding?
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
b***k
发帖数: 2673 | 5 no, I am not.
【在 D*****a 的大作中提到】
: are you kidding?
|
D*****a
发帖数: 2847 | 6 So, are all the inputs to BS formula observable?
【在 b***k 的大作中提到】
: no, I am not.
|
A*****s
发帖数: 13748 | 7 你没理解risk neutral啥意思
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
s*******r
发帖数: 60 | 8 我面GS时被问到过这个，盼解释。
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
s*******r
发帖数: 60 | 9 我认为实际中option 确实用到的在risk neutral space 的定价。就是因为是这个价。
才是公平合理的。至于能不能赚钱，那是另外一回事，取决你对risk的态度，
你要是愿意take risk的话，你就愿意去买，反之，你就不愿意。
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
s*******r
发帖数: 60 | 10 至于为什么能用，具体的数学证明，我就不知道了，盼解释。
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
|
|
j*****4
发帖数: 292 | 11 BS formula is corret only in BS world.
All models are wrong; some models are useful.
-G.E Box.
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
h*y
发帖数: 1289 | 12 在risk neutral world中，个人对risk的态度不影响定价。
换句话说，risk premium等于0，所以我们要用risk free rate来discount。
【在 s*******r 的大作中提到】
: 我认为实际中option 确实用到的在risk neutral space 的定价。就是因为是这个价。
: 才是公平合理的。至于能不能赚钱，那是另外一回事，取决你对risk的态度，
: 你要是愿意take risk的话，你就愿意去买，反之，你就不愿意。
|
n****e
发帖数: 629 | 13 Assuming you're an ib trader, buy/sell options.
How do you hedge your position? Can you construct a riskfree portfolio?
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
f*****y
发帖数: 2 | 14
This is a simple, but interesting question. We always do lot of math such as
solving PDE to get an option price, but many times we are even not
understanding some basic concepts.
To answer your question. option定价和option买卖的价格不是一回事。
There are a lot to say about option定价, but here I ignore the
option定价 and assume that we can obtain the option定价 easily. Even in this
case, an option writer (short position) will need to charge an buyer a
premium in order to make a profit, which can be small or large
【在 s*******r 的大作中提到】
: 至于为什么能用，具体的数学证明，我就不知道了，盼解释。
|
h*y
发帖数: 1289 | 15 Risk Neutral并不是说没有风险，而是说对风险的态度是Neutral的。
市场上的Quote是由Supply/Demand决定的。有了Quote，再通过适当的model，人们可以
imply the underlying distribution, the volatility surface, etc.有了这些东西，
我们就可以对一些exotics进行定价了。
说到交易，derivative marke的paticipants有hedger, arbitrager和 speculator。He
dger是用derivatives来避险，目的不是要赚钱。arbitrager属于空手套白狼型，利用m
arket的inefficiency赚钱，market的走向对其没有影响。speculator对market realiz
ation进行预测，在通过derivative来leverage。
不管用什么样的model来定价，都是基于当前的information对未来的一个expectation，
可是随着时间的推移，realization只是众多Paths中的一条，赚钱的机会一半一半
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
a**n
发帖数: 3801 | 16 .....
好好学习，天天向上。不要乱说。
【在 s*******r 的大作中提到】
: 我认为实际中option 确实用到的在risk neutral space 的定价。就是因为是这个价。
: 才是公平合理的。至于能不能赚钱，那是另外一回事，取决你对risk的态度，
: 你要是愿意take risk的话，你就愿意去买，反之，你就不愿意。
|
A*****s
发帖数: 13748 | 17 其实RN正确的理解，Shreve的VI Ch1就有讲。。。不知道为什么这么多人都不看。。。
西，
He
用m
realiz
expectation，
【在 h*y 的大作中提到】
: Risk Neutral并不是说没有风险，而是说对风险的态度是Neutral的。
: 市场上的Quote是由Supply/Demand决定的。有了Quote，再通过适当的model，人们可以
: imply the underlying distribution, the volatility surface, etc.有了这些东西，
: 我们就可以对一些exotics进行定价了。
: 说到交易，derivative marke的paticipants有hedger, arbitrager和 speculator。He
: dger是用derivatives来避险，目的不是要赚钱。arbitrager属于空手套白狼型，利用m
: arket的inefficiency赚钱，market的走向对其没有影响。speculator对market realiz
: ation进行预测，在通过derivative来leverage。
: 不管用什么样的model来定价，都是基于当前的information对未来的一个expectation，
: 可是随着时间的推移，realization只是众多Paths中的一条，赚钱的机会一半一半
|
b***k
发帖数: 2673 | 18 呵呵，听上去你是理解了NR的真谛啊，
说说看，让我来看看你理解了的真谛是什么？
【在 A*****s 的大作中提到】
: 你没理解risk neutral啥意思
|
t**********a
发帖数: 166 | 19 When you say option pricing, what vol do you want to put into formula?
the market price in option market decides your implied vol.
Of course, you can come up with some other vol, and you might not use the
implied vol.
Then whatever vol you want to use is no longer risk neutral, and it is in
your own risk measure.
To take into account of vol changes, you can't use BS to get risk neutral.
You have to use local vol or stochastic vol. In those models, you will get
more parameters that are not traded |
A*****s
发帖数: 13748 | 20 Shreve第一章就讲了，简化的二叉模型里，不对上行下行的百分比做预期，只求无论上
下都能cover支出，这叫risk neutral
risk neutral不是说定价的时候认为没有risk，而是对risk做一个perfect hedge
这有什么问题么？
至于交易价和RN价的margin，就说明了市场对于risk的preference。。。
这又有什么问题么？
【在 b***k 的大作中提到】
: 呵呵，听上去你是理解了NR的真谛啊，
: 说说看，让我来看看你理解了的真谛是什么？
|
|
|
l****o
发帖数: 2909 | 21 看了这么多帖子，这个是最有水平的了。
【在 t**********a 的大作中提到】
: When you say option pricing, what vol do you want to put into formula?
: the market price in option market decides your implied vol.
: Of course, you can come up with some other vol, and you might not use the
: implied vol.
: Then whatever vol you want to use is no longer risk neutral, and it is in
: your own risk measure.
: To take into account of vol changes, you can't use BS to get risk neutral.
: You have to use local vol or stochastic vol. In those models, you will get
: more parameters that are not traded
|
b***k
发帖数: 2673 | 22 还是你理解的深刻。呵呵。
我提问的原因只是觉着看了那么多书，学了那么多高深的所谓定价理论和方法，
到头来连真正的option买卖价格都不知道怎么来的，听着有点滑稽。
【在 A*****s 的大作中提到】
: Shreve第一章就讲了，简化的二叉模型里，不对上行下行的百分比做预期，只求无论上
: 下都能cover支出，这叫risk neutral
: risk neutral不是说定价的时候认为没有risk，而是对risk做一个perfect hedge
: 这有什么问题么？
: 至于交易价和RN价的margin，就说明了市场对于risk的preference。。。
: 这又有什么问题么？
|
A*****s
发帖数: 13748 | 23 这是损我嘛？交易价是市场trade出来的啊？
【在 b***k 的大作中提到】
: 还是你理解的深刻。呵呵。
: 我提问的原因只是觉着看了那么多书，学了那么多高深的所谓定价理论和方法，
: 到头来连真正的option买卖价格都不知道怎么来的，听着有点滑稽。
|
h*y
发帖数: 1289 | 24 Well, I'm sorry to say I don't agree with you.
Shreve introduces the risk neutral prob but not its defination.
Risk neutrality is one of the risk preferences.
An investor is risk averse if he prefers X0 for sure to a gamble yielding
X0 - dX or X0 + dX with equal probability. An investor who is indifferen
t to this gamble is risk-neutral.
【在 A*****s 的大作中提到】
: Shreve第一章就讲了，简化的二叉模型里，不对上行下行的百分比做预期，只求无论上
: 下都能cover支出，这叫risk neutral
: risk neutral不是说定价的时候认为没有risk，而是对risk做一个perfect hedge
: 这有什么问题么？
: 至于交易价和RN价的margin，就说明了市场对于risk的preference。。。
: 这又有什么问题么？
|
A*****s
发帖数: 13748 | 25 indifferent to gamble就是有了perfect hedge做保证啊
我觉得是一个意思囧
yielding
indifferen
【在 h*y 的大作中提到】
: Well, I'm sorry to say I don't agree with you.
: Shreve introduces the risk neutral prob but not its defination.
: Risk neutrality is one of the risk preferences.
: An investor is risk averse if he prefers X0 for sure to a gamble yielding
: X0 - dX or X0 + dX with equal probability. An investor who is indifferen
: t to this gamble is risk-neutral.
|
a*********a
发帖数: 3656 | 26 u guys are talking about different context.
your risk neutral is the one appearing in portoflion optimization
literatures. his is the one in derivative pricing.
in the context of option pricing, I agree with him.
In stochastic asset pricing, risk neutral means you hedge away all the risks
in a complete market.
therefore you do not care if the underlying (risk factors) will move, by how
much and with what probability.
the key is market is complete so you can hedge away all the risks, and end
up w
【在 h*y 的大作中提到】
: Well, I'm sorry to say I don't agree with you.
: Shreve introduces the risk neutral prob but not its defination.
: Risk neutrality is one of the risk preferences.
: An investor is risk averse if he prefers X0 for sure to a gamble yielding
: X0 - dX or X0 + dX with equal probability. An investor who is indifferen
: t to this gamble is risk-neutral.
|
a*********a
发帖数: 3656 | 27 in context of risk neutral, i.e. no arb, derive pricing, it is not a gamble
at all.
you know before hand your cash flow is flat no matter what happened as long
as you follow the dynamic hedging indicated by the model.
but the models are all wrong one way or the other.
in portfolio theory, risk neutral means knowing there s possibility to loose money but still do it, as long as the price is fair.
【在 A*****s 的大作中提到】
: indifferent to gamble就是有了perfect hedge做保证啊
: 我觉得是一个意思囧
:
: yielding
: indifferen
|
f*****y
发帖数: 2 | 28 The definition on risk neutral preference you provided is used in the
utility theory of economics. However, for the risk neutral probability in
finance I feel there are some differences.
In finance, the risk neutral probability or measure comes from the idea that
in the complete market we can perfectly replicate the the option,
so the option price should satisfy the martingale condition and discounted
at the risk free rate. It has nothing to do with preferences and it is just
changing the physic
【在 h*y 的大作中提到】
: Well, I'm sorry to say I don't agree with you.
: Shreve introduces the risk neutral prob but not its defination.
: Risk neutrality is one of the risk preferences.
: An investor is risk averse if he prefers X0 for sure to a gamble yielding
: X0 - dX or X0 + dX with equal probability. An investor who is indifferen
: t to this gamble is risk-neutral.
|
A*****s
发帖数: 13748 | 29 这三个帖子很长眼啊！终于知道为什么有时候，不知道有些人说RN啥意思。。。
原来是经济学里的RN，和finance的不太一样
that
just
gamble
【在 f*****y 的大作中提到】
: The definition on risk neutral preference you provided is used in the
: utility theory of economics. However, for the risk neutral probability in
: finance I feel there are some differences.
: In finance, the risk neutral probability or measure comes from the idea that
: in the complete market we can perfectly replicate the the option,
: so the option price should satisfy the martingale condition and discounted
: at the risk free rate. It has nothing to do with preferences and it is just
: changing the physic
|
a*********a
发帖数: 3656 | 30 in both context, one consequence is as another poster said, the cash flow is
discounted with the risk neutral discount curve (at risk free rate, no
extra drift in the discount).
A heavily risk averse investor should be perfectly happy to engage in an
option trade as long as he can access the hedging instruments without
friction.
【在 A*****s 的大作中提到】
: 这三个帖子很长眼啊！终于知道为什么有时候，不知道有些人说RN啥意思。。。
: 原来是经济学里的RN，和finance的不太一样
:
: that
: just
: gamble
|
|
|
s*******r
发帖数: 60 | 31 看到版上牛人这么多，再发个GS面试题出来讨论讨论。
"why the delta hedging cost is not zero?"
我给面试官的解释是 from Black Scholes theory, we can construct a self-
financing portfolio by delta hedging, the hedging cost should be zero.
However, because the stochastic property of the stock price, we cann't do
delta hedging continuously and we can only do the hedging after we know and
wait the stock price cross a level. Thus a small extra cost will be incurred
and a delta hedge is no long riskless. In real world, we adjust the he
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
a*********a
发帖数: 3656 | 32 hard to determine what he had in mind. I think your answer is valid. Another
thing if we assume friction is 0, might be that vol is not constant, so
when spot moves, you delta hedges start to show higher order tracking errors on top of the BS gamma.
Next time, if an interviewer disagrees with your answer, ask what he thinks
is right. what s the error he found in your logic. this way you learn on
spot and don't have to second guess him later.
and
incurred
hedging
【在 s*******r 的大作中提到】
: 看到版上牛人这么多，再发个GS面试题出来讨论讨论。
: "why the delta hedging cost is not zero?"
: 我给面试官的解释是 from Black Scholes theory, we can construct a self-
: financing portfolio by delta hedging, the hedging cost should be zero.
: However, because the stochastic property of the stock price, we cann't do
: delta hedging continuously and we can only do the hedging after we know and
: wait the stock price cross a level. Thus a small extra cost will be incurred
: and a delta hedge is no long riskless. In real world, we adjust the he
|
s*******r
发帖数: 60 | 33 Thank you!
Another
errors on top of the BS gamma.
thinks
【在 a*********a 的大作中提到】
: hard to determine what he had in mind. I think your answer is valid. Another
: thing if we assume friction is 0, might be that vol is not constant, so
: when spot moves, you delta hedges start to show higher order tracking errors on top of the BS gamma.
: Next time, if an interviewer disagrees with your answer, ask what he thinks
: is right. what s the error he found in your logic. this way you learn on
: spot and don't have to second guess him later.
:
: and
: incurred
: hedging
|
t**********a
发帖数: 166 | 34 not sure what is "hedging cost"
If it meant the slippage and bid/ask spread, that is due that your delta
trading will move the price against your
target price, resulting in costing more money;
or it meant gamma PNL, that is due to realized vol is different from implied.
Actually what you try to say might be close to slippage, but it is not due
to "noncasusality" (i.e. not know the
price before delta hedging). The delta is a strategy based on all the
information we know (dW = Wt - W(t-dt),
not Wt
【在 s*******r 的大作中提到】
: 看到版上牛人这么多，再发个GS面试题出来讨论讨论。
: "why the delta hedging cost is not zero?"
: 我给面试官的解释是 from Black Scholes theory, we can construct a self-
: financing portfolio by delta hedging, the hedging cost should be zero.
: However, because the stochastic property of the stock price, we cann't do
: delta hedging continuously and we can only do the hedging after we know and
: wait the stock price cross a level. Thus a small extra cost will be incurred
: and a delta hedge is no long riskless. In real world, we adjust the he
|
s*******r
发帖数: 60 | 35 The interviewer said we assume the market is complete,no transaction cost
and the stock price follow a log normal.
I am seriously considering what you said the gamma PNL issue.
Thank you!
implied.
【在 t**********a 的大作中提到】
: not sure what is "hedging cost"
: If it meant the slippage and bid/ask spread, that is due that your delta
: trading will move the price against your
: target price, resulting in costing more money;
: or it meant gamma PNL, that is due to realized vol is different from implied.
: Actually what you try to say might be close to slippage, but it is not due
: to "noncasusality" (i.e. not know the
: price before delta hedging). The delta is a strategy based on all the
: information we know (dW = Wt - W(t-dt),
: not Wt
|
p******i
发帖数: 1358 | 36 then discrete hedging
【在 s*******r 的大作中提到】
: The interviewer said we assume the market is complete,no transaction cost
: and the stock price follow a log normal.
: I am seriously considering what you said the gamma PNL issue.
: Thank you!
:
: implied.
|
p******i
发帖数: 1358 | 37 NR reflects the market consensus of the underlying distribution for a future
time. If someone thinks he/she has ability to out-guess the market and is
willing to take the risk, he/she can of course trade his/her own measure
against the market RN measure.
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
h*y
发帖数: 1289 | 38 I'd like to stress the following points:
1. "Risk neutral" and "Risk free" are two different concepts
2. Risk neutral probabilities exist if and only if there is no
arbitrage.
3. The risk neutral probabilities are unique if and only if
the market is complete.
4. Under risk neutral measure, or say in the risk neutral world,
investors are indifferent to risk, requesting no additional
compensation for risk(risk premium), therefore, CFs are discounted at
risk free rate.
the
probability in
idea that
【在 f*****y 的大作中提到】
: The definition on risk neutral preference you provided is used in the
: utility theory of economics. However, for the risk neutral probability in
: finance I feel there are some differences.
: In finance, the risk neutral probability or measure comes from the idea that
: in the complete market we can perfectly replicate the the option,
: so the option price should satisfy the martingale condition and discounted
: at the risk free rate. It has nothing to do with preferences and it is just
: changing the physic
|
h*y
发帖数: 1289 | 39 I don't think you fully understand what I said.
Actually, it's not I said. I copied from Rubinstein's notes. It took me
a while to digest it, too.
the risks
by how
and end
【在 a*********a 的大作中提到】
: u guys are talking about different context.
: your risk neutral is the one appearing in portoflion optimization
: literatures. his is the one in derivative pricing.
: in the context of option pricing, I agree with him.
: In stochastic asset pricing, risk neutral means you hedge away all the risks
: in a complete market.
: therefore you do not care if the underlying (risk factors) will move, by how
: much and with what probability.
: the key is market is complete so you can hedge away all the risks, and end
: up w
|
a*********a
发帖数: 3656 | 40 The only thing we can do here is examing the assumptions underlying the BS
dynamic hedging strategy one by one.
the interviewer clearly stated some of them hold. especially the stock price
process.
if the stock is assumed to be log normal, then it rules out vol not being a
constant.
I think it also ruled out deviation from BS caused by the hedging trades
impact the spot price. since what ever impact it is, it is included in the
log normal process anyway. whether or not you trade, the distributio
【在 s*******r 的大作中提到】
: The interviewer said we assume the market is complete,no transaction cost
: and the stock price follow a log normal.
: I am seriously considering what you said the gamma PNL issue.
: Thank you!
:
: implied.
|
|
|
h*y
发帖数: 1289 | 41 Risk neutral pricing can be done without hedging.
Once the risk neutral probabilities (or state prices) are given, you
can do pricing.
For example, in Monte Carlo simulation, you don't need to hedge an
option first.
gamble
as long
to loose money but still do it, as long as the price is fair.
【在 a*********a 的大作中提到】
: in context of risk neutral, i.e. no arb, derive pricing, it is not a gamble
: at all.
: you know before hand your cash flow is flat no matter what happened as long
: as you follow the dynamic hedging indicated by the model.
: but the models are all wrong one way or the other.
: in portfolio theory, risk neutral means knowing there s possibility to loose money but still do it, as long as the price is fair.
|
a*********a
发帖数: 3656 | 42 I think I understood you alright.
your first post defined risk neutral as a preference, which I think is the
wrong context in the original discussion.
then you pasted some stuff presumably from Rubinstein's notes, which defines
risk neutral as a measure which is relevant here.
【在 h*y 的大作中提到】
: I don't think you fully understand what I said.
: Actually, it's not I said. I copied from Rubinstein's notes. It took me
: a while to digest it, too.
:
: the risks
: by how
: and end
|
a*********a
发帖数: 3656 | 43 don't just copy notes. think.
pricing can be done in any measure!
I can say in a bloody ass measure a call on IBM striking at 1MM a share
worth 1MM a contract.
The price derived from risk neutral measure means nothing if the underlying
can not be traded to hedge, i.e. if the market is not complete!
what makes risk neutral measure so special?
a risk neutral investor will be willing to buy a call at risk neutral price
with out hedge.
a risk averse investor will not buy a call with out hedge at ris
【在 h*y 的大作中提到】
: Risk neutral pricing can be done without hedging.
: Once the risk neutral probabilities (or state prices) are given, you
: can do pricing.
: For example, in Monte Carlo simulation, you don't need to hedge an
: option first.
:
: gamble
: as long
: to loose money but still do it, as long as the price is fair.
|
h*y
发帖数: 1289 | 44 Well, Rubinstein defines "Risk neutral" as a prefrence in his notes. It is b
ecause the risk neutral preference, we dicount CFs at risk free rate without
risk premium.
defines
【在 a*********a 的大作中提到】
: I think I understood you alright.
: your first post defined risk neutral as a preference, which I think is the
: wrong context in the original discussion.
: then you pasted some stuff presumably from Rubinstein's notes, which defines
: risk neutral as a measure which is relevant here.
|
h*y
发帖数: 1289 | 45 Easy, easy.
You're talking about no arbitrage pricing, not risk neutral pricing. They ar
e different.
Btw, I don't think your IBM 1MM call is a good example.
underlying
price
【在 a*********a 的大作中提到】
: don't just copy notes. think.
: pricing can be done in any measure!
: I can say in a bloody ass measure a call on IBM striking at 1MM a share
: worth 1MM a contract.
: The price derived from risk neutral measure means nothing if the underlying
: can not be traded to hedge, i.e. if the market is not complete!
: what makes risk neutral measure so special?
: a risk neutral investor will be willing to buy a call at risk neutral price
: with out hedge.
: a risk averse investor will not buy a call with out hedge at ris
|
l****o
发帖数: 2909 | 46 呵呵，兄台的帖子，水平果然不一样。
implied.
【在 t**********a 的大作中提到】
: not sure what is "hedging cost"
: If it meant the slippage and bid/ask spread, that is due that your delta
: trading will move the price against your
: target price, resulting in costing more money;
: or it meant gamma PNL, that is due to realized vol is different from implied.
: Actually what you try to say might be close to slippage, but it is not due
: to "noncasusality" (i.e. not know the
: price before delta hedging). The delta is a strategy based on all the
: information we know (dW = Wt - W(t-dt),
: not Wt
|
p******i
发帖数: 1358 | 47 IBM 1MM call is indeed a very good example
They ar
【在 h*y 的大作中提到】
: Easy, easy.
: You're talking about no arbitrage pricing, not risk neutral pricing. They ar
: e different.
: Btw, I don't think your IBM 1MM call is a good example.
:
: underlying
: price
|
h*y
发帖数: 1289 | 48 他想说pricing可以在任何measure下进行，这点我完全同意。但是Change of measure不
应该影响最终price的结果。
对于那个IBM 1MM call,因为不是在risk neutral measure,所以必须考虑risk adjustm
ent，得到的pricing结果和在risk neutral measure下得到的结果是必须是一致的。
关于risk neutral的问题，我想大家还是看看wikipedia上是怎么说的吧。http://en.w
ikipedia.org/wiki/Risk-neutral_measure
【在 p******i 的大作中提到】
: IBM 1MM call is indeed a very good example
:
: They ar
|
p******i
发帖数: 1358 | 49 using who's utility function?
say we both agreed on this bloody ass measure other than RN measure
but you are risk averse and I am risk seeking
and you are telling me that the 'value' of the call should be the same for
both of us?
think it again
measure不
adjustm
【在 h*y 的大作中提到】
: 他想说pricing可以在任何measure下进行，这点我完全同意。但是Change of measure不
: 应该影响最终price的结果。
: 对于那个IBM 1MM call,因为不是在risk neutral measure,所以必须考虑risk adjustm
: ent，得到的pricing结果和在risk neutral measure下得到的结果是必须是一致的。
: 关于risk neutral的问题，我想大家还是看看wikipedia上是怎么说的吧。http://en.w
: ikipedia.org/wiki/Risk-neutral_measure
|
h*y
发帖数: 1289 | 50 I don't want to waste more time on this. Please click the link and read it c
arefully.
Thank you very much.
【在 p******i 的大作中提到】
: using who's utility function?
: say we both agreed on this bloody ass measure other than RN measure
: but you are risk averse and I am risk seeking
: and you are telling me that the 'value' of the call should be the same for
: both of us?
: think it again
:
: measure不
: adjustm
|
|
|
p******i
发帖数: 1358 | 51 neither do I
you are very welcome
it c
【在 h*y 的大作中提到】
: I don't want to waste more time on this. Please click the link and read it c
: arefully.
: Thank you very much.
|
n****e
发帖数: 629 | 52 这个讨论很不错
推荐大家看看Derman的Notes
http://www.ederman.com/new/docs/smile-lecture3.pdf
专门讲到了如何hedge,以及spread/realized vol对hedge的影响
【在 b***k 的大作中提到】
: 今天k书的时候想到的，
: 我们常说的用什么BS啊，这个模型那个方法给option pricing，
: 那这个定出的价格和交易市场上option真正买进卖出的价格是一回事吗？
: 如果是一回事，那有个问题我就不明白了，
: 不是说都是基于risk neutral定价的吗，这样的话定出的期权理论上是
: 没有风险的，也就没有赚头可言了，那谁还会去买？
: 还是说各家有各家的模型给derivative定价，然后市场上买卖的价格是另一回事？
: 如果是这样，我觉得还有点搞头，可以利用差价啊什么来投机。
|
