n****w
发帖数: 156 | 1 既然有Feynman-Kac formula
为什么不直接得出PDE
看到的BS的解法都是或者建立一个不含dW项的portfolio然后得出PDE 或者用risk
neutral measure来取expected discount | j***e
发帖数: 72 | 2 有变为标准扩散方程来解的，但是，这里有边界条件，所以，也不容易。虽然原理上清
楚，具体数学很繁琐的。
【在 n****w 的大作中提到】
: 既然有Feynman-Kac formula
: 为什么不直接得出PDE
: 看到的BS的解法都是或者建立一个不含dW项的portfolio然后得出PDE 或者用risk
: neutral measure来取expected discount
| b******w
发帖数: 52 | 3 I think one of BS's contributions is to construct a replicating portofio to
replicating the option. A bold argument is that the instanenous rate to
apply for that portfolio is r, as a by-product, this means the drfit term
for the stock GBM dynamics is r, not \mu. Thus, you can safely assume that
in the risk neutral world,
ds/s = r dt + \sigma dw. When you reach this stage, you can delightly apply
Feynman-Kay formula to conclude that BS's PDE. But BS are the first few to
realize that.
When BS der
【在 n****w 的大作中提到】
: 既然有Feynman-Kac formula
: 为什么不直接得出PDE
: 看到的BS的解法都是或者建立一个不含dW项的portfolio然后得出PDE 或者用risk
: neutral measure来取expected discount
| i******d
发帖数: 54 | 4 yes,portfolio replication is the most important contributuion
to
apply
are
【在 b******w 的大作中提到】
: I think one of BS's contributions is to construct a replicating portofio to
: replicating the option. A bold argument is that the instanenous rate to
: apply for that portfolio is r, as a by-product, this means the drfit term
: for the stock GBM dynamics is r, not \mu. Thus, you can safely assume that
: in the risk neutral world,
: ds/s = r dt + \sigma dw. When you reach this stage, you can delightly apply
: Feynman-Kay formula to conclude that BS's PDE. But BS are the first few to
: realize that.
: When BS der
| n****w
发帖数: 156 | 5 Thanks for clarifying!
to
apply
are
【在 b******w 的大作中提到】
: I think one of BS's contributions is to construct a replicating portofio to
: replicating the option. A bold argument is that the instanenous rate to
: apply for that portfolio is r, as a by-product, this means the drfit term
: for the stock GBM dynamics is r, not \mu. Thus, you can safely assume that
: in the risk neutral world,
: ds/s = r dt + \sigma dw. When you reach this stage, you can delightly apply
: Feynman-Kay formula to conclude that BS's PDE. But BS are the first few to
: realize that.
: When BS der
|
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