c**********e
发帖数: 2007 | 1 Suppose two stocks S1 and S2 each follows its GBM, with the instaneous
correlation of the two brownian motions rho.
An option pays max(S_{1T}-K, S_{2T}-K, 0) at time T. The price of the option
should be exp(-rT)*E[max(S_{1T}-K, S_{2T}-K, 0)]. This is an analytical
form as log(S1) and log(S2) has joint normal distribution.
我的问题是，这个期权价格能否简化。 |
m******g
发帖数: 12 | 2 the price is the sum of an ordinary call option price and an exchange option
price (Margrabe formula). |
z****i
发帖数: 406 | 3 K=0的话，有closed form solution, google 'Margrabe formula'.
If K is not 0, there is no closed form solution. check out 'pricing and
hedging spread options in a log-normal model' and following papers by Rene
Carmona and Valdo Durrleman. |
c**********e
发帖数: 2007 | 4 谢谢。看来，二维正则分布在扇形上的积分，只有扇形圆心与分布中心重合时才可以简
化。
【在 z****i 的大作中提到】
: K=0的话，有closed form solution, google 'Margrabe formula'.
: If K is not 0, there is no closed form solution. check out 'pricing and
: hedging spread options in a log-normal model' and following papers by Rene
: Carmona and Valdo Durrleman.
|
z****i
发帖数: 406 | 5 好高深的解释啊，呵呵。
我是硬算的，发现要对正态分布的cdf积分，所以没有closed form的解。
如果是K＝0的话，用change of numeraire，然后套Black Scholes公式，很容易就把结
果写出来了。
【在 c**********e 的大作中提到】
: 谢谢。看来，二维正则分布在扇形上的积分，只有扇形圆心与分布中心重合时才可以简
: 化。
|
l***u
发帖数: 91 | 6 没有显示解 半显示解是对BS进行积分
option
【在 c**********e 的大作中提到】
: Suppose two stocks S1 and S2 each follows its GBM, with the instaneous
: correlation of the two brownian motions rho.
: An option pays max(S_{1T}-K, S_{2T}-K, 0) at time T. The price of the option
: should be exp(-rT)*E[max(S_{1T}-K, S_{2T}-K, 0)]. This is an analytical
: form as log(S1) and log(S2) has joint normal distribution.
: 我的问题是，这个期权价格能否简化。
|
p*****k
发帖数: 318 | 7 probably should read the reference by zhucai first before
i comment, but i fail to see the relevance of the
spread option here.
in any case, a call on either the maximum (or minimum)
of two stocks can be expressed using bivariate normal c.d.f..
see e.g., Stulz (1982)
http://dx.doi.org/10.1016/0304-405X(82)90011-3
similar to 1d normal c.d.f., good algorithms exist to
evaluate it numerically:
http://www.math.wsu.edu/faculty/genz/papers/bvnt/bvnt.html |
z****i
发帖数: 406 | 8 sorry i just realized i misread the problem, i thought the payoff was max(S_
1-S_2-K, 0)
【在 p*****k 的大作中提到】
: probably should read the reference by zhucai first before
: i comment, but i fail to see the relevance of the
: spread option here.
: in any case, a call on either the maximum (or minimum)
: of two stocks can be expressed using bivariate normal c.d.f..
: see e.g., Stulz (1982)
: http://dx.doi.org/10.1016/0304-405X(82)90011-3
: similar to 1d normal c.d.f., good algorithms exist to
: evaluate it numerically:
: http://www.math.wsu.edu/faculty/genz/papers/bvnt/bvnt.html
|
