w*********n
发帖数: 48 | 1 Assume B-S model and a porfolio is now Vega neutral
Will it be Gamma neutral?
大牛来说说吧 |
k****o
发帖数: 11 | 2 This problem can be found in Mark Joshi's book:
gamma neutral is equivalent to
\sum_{i=1}^n N(d_1(i))=0 (assuming time to maturity and vol are non-zero)
d_1(i) stands for d_1 for different options in your portfolio.
Hence, by comparing with formula from vega, that means
vega neutral as well. |
u****g
发帖数: 402 | 3 请问在 Mark Joshi的那一页？
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【在 k****o 的大作中提到】
: This problem can be found in Mark Joshi's book:
: gamma neutral is equivalent to
: \sum_{i=1}^n N(d_1(i))=0 (assuming time to maturity and vol are non-zero)
: d_1(i) stands for d_1 for different options in your portfolio.
: Hence, by comparing with formula from vega, that means
: vega neutral as well.
|
l*******1
发帖数: 113 | 4 vega1 = gamma1 * s^2 * vol * T1
vega2= gamma2 *s^2 * vol * T2
sum(vega) = 0 = s^2*vol*sum(gamma*T）
if T is the same, then vega neutral = gamma neutral.
If T is different, then its not equivalent. |
t**********a
发帖数: 166 | 5 vol can be different for different strike, plus with vol smile, calculated
gamma is no longer black-scholes gamma even using BS pricer ...
【在 l*******1 的大作中提到】
: vega1 = gamma1 * s^2 * vol * T1
: vega2= gamma2 *s^2 * vol * T2
: sum(vega) = 0 = s^2*vol*sum(gamma*T）
: if T is the same, then vega neutral = gamma neutral.
: If T is different, then its not equivalent.
|
