g***e
发帖数: 577 | 1 If stock A follows geometric BM, stock B follows GBM as well.
The sum (A+B) doesn't follow GBM in general, then why is it valid
to price stock index derivative using GBM? | b*****n
发帖数: 14 | 2 why not? you can use affine transformation.
【在 g***e 的大作中提到】
: If stock A follows geometric BM, stock B follows GBM as well.
: The sum (A+B) doesn't follow GBM in general, then why is it valid
: to price stock index derivative using GBM?
| n****y
发帖数: 4 | 3 what do you mean? could you give a more detail explanation? Thanks. | g***e
发帖数: 577 | 4 I mean,
basicly, A stock value is log normal at time T, so is B,
but A+B is not lognormal in general...
Isn't this a problem?
【在 n****y 的大作中提到】
: what do you mean? could you give a more detail explanation? Thanks.
| d*******n
发帖数: 524 | 5
I think the point that stock index follows GBM is an independent assumption
from the very beginning, i.e. an ab initio assumption, instead of being a
derivative conclusion from the assumption that the included stocks are
respectively following GBM. And the two assumptions are not completely
consistent.
Actually, in a real case,
1) None of the stock prices really follows GBM exactly.
2) The correlations between stock prices are quite complicated.
In such case, it is practical and reasonable to
【在 g***e 的大作中提到】
: If stock A follows geometric BM, stock B follows GBM as well.
: The sum (A+B) doesn't follow GBM in general, then why is it valid
: to price stock index derivative using GBM?
| j****e
发帖数: 140 | 6
assumption
proof? source?
index
as) assuming stock
【在 d*******n 的大作中提到】
:
: I think the point that stock index follows GBM is an independent assumption
: from the very beginning, i.e. an ab initio assumption, instead of being a
: derivative conclusion from the assumption that the included stocks are
: respectively following GBM. And the two assumptions are not completely
: consistent.
: Actually, in a real case,
: 1) None of the stock prices really follows GBM exactly.
: 2) The correlations between stock prices are quite complicated.
: In such case, it is practical and reasonable to
| p*******i
发帖数: 309 | 7 谢谢指点， 不说出来还真的没觉得自己知道这个问题。哈哈 | n****y
发帖数: 4 | 8 I understood what you meant. But when I asked, I was actually asking the
person who mentioned the affine transform....I don't know how to transform
it. So, if it really can be transformed to GBM, I would really like to know
how. Thanks.
【在 g***e 的大作中提到】
: I mean,
: basicly, A stock value is log normal at time T, so is B,
: but A+B is not lognormal in general...
: Isn't this a problem?
| n****y
发帖数: 4 | 9 Why the error of this assumption is just as big as (or as small
as) assuming stock is GBM? if stock is very close to GBM, then, index can't
be, right? Or did I miss something?
assumption
proof? source?
index
as) assuming stock
【在 d*******n 的大作中提到】
:
: I think the point that stock index follows GBM is an independent assumption
: from the very beginning, i.e. an ab initio assumption, instead of being a
: derivative conclusion from the assumption that the included stocks are
: respectively following GBM. And the two assumptions are not completely
: consistent.
: Actually, in a real case,
: 1) None of the stock prices really follows GBM exactly.
: 2) The correlations between stock prices are quite complicated.
: In such case, it is practical and reasonable to
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