l****w
发帖数: 10 | 1 想请教一下这里的大牛们，
omega= call option elasticity =(dc/ds)*（s/c）随着 s 增加 递减的图是怎么得来的？
(dc/ds)*（s/c）>1 证明得非常明白，但是为什么随着 s 增加，call option elasticity=(dc/ds)*
（s/c） 递减，我看到 Mcdonald ,hull 只说啦intution,然后给拉numerical example.
但是为什么d[(dc/ds)*（s/c）]/ds <0, 我证明拉好久都没弄出来。这里的牛人多，我
想确认以下，是不是肯定不能证明，只能numerical 画图？如果能证明请大牛给我指点
一下吧。谢谢 | l****w
发帖数: 10 | | p*****k
发帖数: 318 | 3 EDITED: sorry the proof below is not correct.
to draw the conclusion that x decreases as S increases, what matters is whether the FRACTIONAL increase of the first term is larger than the second term, i.e., whether
[N(d1) + S*N'(d1)*d(d1)/dS]/[S*N(d1)] > [K*e^{-r(T-t)}*N'(d2)*d(d2)/dS]/[K*e^{-r(T-t)}*N(d2)].
i have not found an easy way to prove this, but i did find one reference in case anyone interested:
Borell, C.(1998) Geometric Inequalities in Option Pricing, MSRI Publications 34, 29–51
whic | m*******n
发帖数: 305 | 4 This is a very cool proof, thanks! | l****w
发帖数: 10 | 5 请教 pcasnik，不知道那里错啦？
那应该从什么direction 去证明？谢谢
whether the FRACTIONAL increase of the first term is larger than the second
term, i.e., whether
*e^{-r(T-t)}*N(d2)].
in case anyone interested:
Publications 34, 29–51
is that the payoff function of a call (S-K)^+ is log-concave, which is very
easy to verify.
【在 p*****k 的大作中提到】
: EDITED: sorry the proof below is not correct.
: to draw the conclusion that x decreases as S increases, what matters is whether the FRACTIONAL increase of the first term is larger than the second term, i.e., whether
: [N(d1) + S*N'(d1)*d(d1)/dS]/[S*N(d1)] > [K*e^{-r(T-t)}*N'(d2)*d(d2)/dS]/[K*e^{-r(T-t)}*N(d2)].
: i have not found an easy way to prove this, but i did find one reference in case anyone interested:
: Borell, C.(1998) Geometric Inequalities in Option Pricing, MSRI Publications 34, 29–51
: whic
| p*****k
发帖数: 318 | 6 i meant the original proof below the line is not correct.
(even if A(S) increases faster than B(S) as S increases, it does not mean B/A decreases as S increases. what matters is the fractional change of A and B)
for a proof, you could check Borell(1998), the reference listed above. |
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