请教关于bs模型的问题

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

已知一只无分红股票价格S（t）满足 ds(t)=s(t)[udt+odb(t)],t>=0
其中b(t)为标准布朗运动，用r表示市场无风险连续复利。基于该股票的欧式看涨期权，期限为t，执行价为s(0)e的rt次方。已知：1、s（0）=14
2、t=9
3、u=0.2
4、lns(t)的均值为0.12t
根据bs公式、该期权的价格为？
求各位大神，也可以给个思路。多谢

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：bs公式 布朗运动 股票价格 连续复利 无风险 模型

希望大神们慷慨赐教啊

yayuncao 发表于 2013-4-8 21:55
希望大神们慷慨赐教啊

d1=log(S(0)/K)+(r+0.5*sigma^2)t/(sigma*sqrt(t))

K=S(0)exp(rt)

=> d1=0.5*sigma*sqrt(t), d2=-0.5*sigma*sqrt(t)

lns(t)~N[lns(0)+(u-0.5*sigma^2)t, sigma^2*t], I think here the mean of lns(t)=0.12t should refer to
(u-0.5*sigma^2)t otherwise you have no solution. Now you get sigma

now you have sigma, t and S(0)

so that you have d1 and d2.

BS price=S(0)N(d1)-Kexp(-rt)N(d2)

K=S(0)exp(rt)

option price=S(0)N(d1)-S(0)N(d2)

Everything is known. You can get the price.

Why should lns(t)=0.12t  be   (u-0.5*sigma^2)t  instead of  lns(0)+(u-0.5*sigma^2)t?    Just beginning to learn derivatives pricing, so the questions  are  very naive.I hope more guidance.Thank you very much.

yayuncao 发表于 2013-4-10 12:27
Why should lns(t)=0.12t  be   (u-0.5*sigma^2)t  instead of  lns(0)+(u-0.5*sigma^2)t?    Just beginni ...

In that case, do you think you can solve this equation?

a+bt=ct, if a is not zero.  They cannot be equal for any t. Just for some specific time t.

You  are  right ,but s(0)=14 is given... Am I right ?

yayuncao 发表于 2013-4-10 22:55
You  are  right ,but s(0)=14 is given... Am I right ?

Absolutely