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】![](/moin_static193/solenoid/img/up.png) : 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.
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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】![](/moin_static193/solenoid/img/up.png) : 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。
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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】![](/moin_static193/solenoid/img/up.png) : 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】![](/moin_static193/solenoid/img/up.png) : 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
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