求问bs微分方程

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

求问，连续复利，是把bs微分方程的r变成e的r次方减1，或者还是原来的微分方程？
谢谢！！

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：微分方程 连续复利

原来的

Chemist_MZ 发表于 2013-5-31 04:14
原来的

能否解释一下？谢谢

nkuxxw 发表于 2013-5-31 04:25
能否解释一下？谢谢

Ok, for BS model, if you want to get the PDE, you have to form a self financing portfolio using a option, a stock and a bond.

The bond( strictly: Money Market Account) follows the process dB=rBdt and the stock follows the well-known GBM ds=muSdt+sigmaSdw.

You see that dB=rBdt is an ODE whose solution is just B(0)exp(rt) which is the same as using continuously compounding rate.

For continuous time models, we all use continuous compounding rates.

This homework is just let you to strictly go over the derivation of the BS model. Continuously compouding is not a new condition but some thing that does not want to cause any confusion. You can just ignore it.

best,

Chemist_MZ 发表于 2013-5-31 04:47
Ok, for BS model, if you want to get the PDE, you have to form a self financing portfolio using a  ...

got it.  thanks very much!

人家推导的时候，无风险债券本来就是以连续复利算的。