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Quant版 - A question about BS
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话题: bs话题: price话题: d1话题: d2话题: kexp
进入Quant版参与讨论
1 (共1页)
D******4
发帖数: 47
1
For a European stock option, which has payoff max(S_T-K,0), then the BS
price would be:
C1 = SN(d1)-Kexp(-rT)N(d2).
On the other hand, we know the forward price of the stock at time T would
converges to the stock price, i.e. F_T=S_T, where F_T is the forward price.
Then the BS would give us:
C2 = FN(D1)-Kexp(-rT)N(D2).
I think these call prices should be the same. My question is, is there a
strictly proof to say C1=C2? (Can I assume the volatility used in the first
method be the same of the second method? I don't think so....)
Thanks very much.
D******4
发帖数: 47
2
or is there a logic flaw above? Thanks for clarify.
L**********u
发帖数: 194
3
去看看shreve书的第9章就明白了究竟什么是price了。
搞清楚了price的定义之后,你自己就明白你的问题了。呵呵
D******4
发帖数: 47
4
Right. Thanks. I made a stupid mistake on numeriare.

【在 L**********u 的大作中提到】
: 去看看shreve书的第9章就明白了究竟什么是price了。
: 搞清楚了price的定义之后,你自己就明白你的问题了。呵呵

w******i
发帖数: 503
5
what is the problem? what are D1, D2?

.
first

【在 D******4 的大作中提到】
: For a European stock option, which has payoff max(S_T-K,0), then the BS
: price would be:
: C1 = SN(d1)-Kexp(-rT)N(d2).
: On the other hand, we know the forward price of the stock at time T would
: converges to the stock price, i.e. F_T=S_T, where F_T is the forward price.
: Then the BS would give us:
: C2 = FN(D1)-Kexp(-rT)N(D2).
: I think these call prices should be the same. My question is, is there a
: strictly proof to say C1=C2? (Can I assume the volatility used in the first
: method be the same of the second method? I don't think so....)

1 (共1页)
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话题: bs话题: price话题: d1话题: d2话题: kexp