i*****l
发帖数: 50 | 1 要是哪位有第5版以上的solution manual就更好了
是书后的一道习题
show that the Garch(1,1) model
delta_n^2=w+\alpha u_{n-1}^2 +\beta delta_{n-1}^2
is equivalent to the stochastic volatility model
dV = a(V_L-V)dt + \xi V dz
where V is the squar of the volatility .
a= 1-\alpha-\beta V_L=w/(1-\alpha-\beta) \xi=\alpha \sqrt{2}
请问怎么导出下面这个SDE呢
3x | t*****a
发帖数: 90 | 2 dont waste ur time on it... u wont be asked such question unless u claim
yourself an expert on garch on interview | i*****l
发帖数: 50 | 3 I am just so interested in this problem...
maybe you are right it just waste my time..
【在 t*****a 的大作中提到】
: dont waste ur time on it... u wont be asked such question unless u claim
: yourself an expert on garch on interview
| h*******n
发帖数: 24 | 4 哎,实在看不懂你的题目....
我去书上找到了原题....首先我用sigma代替你的delta,因为后面要用到delta,避免重
复.
解题如下．(这个打字太麻烦,只简单叙述)
sigma_n^2=w+alpha*u_(n-1)^2+beta*sigma_(n-1)^2
所以有
sigma_n^2-sigma_(n-1)^2=w+(beta-1)*sigma_(n-1)^2+alpha*u_(n-1)^2
然后,算出u_(n-1)^2的mean和s.d.
再令deltaV=sigma_n^2-sigma_(n-1)^2, V=sigma_(n-1)^2
Since a= 1-\alpha-\beta V_L=w/(1-\alpha-\beta)
aV_L=w, xi = a*sqrt(2)
所以 deltaV=a*(V_L-V)+xi*epsilon*V, where epsilon is a r.v. from std. normal
dist.
最后, 你代入delta_t, 就可以了. | i*****l
发帖数: 50 | 5 Thank you so much for your detailed answer.
Yes, that is the idea. But I have 2 questions:
1. How can you get deltaV=a*(V_L-V)+ xi*epsilon*V?
u_{n-1}^2 is not std normal dist. any more.
2. how can we add delta_t in the above equation?
With all due respect, this solution, which is also similar to mine, is not a
mathematical derivation.
normal
【在 h*******n 的大作中提到】
: 哎,实在看不懂你的题目....
: 我去书上找到了原题....首先我用sigma代替你的delta,因为后面要用到delta,避免重
: 复.
: 解题如下．(这个打字太麻烦,只简单叙述)
: sigma_n^2=w+alpha*u_(n-1)^2+beta*sigma_(n-1)^2
: 所以有
: sigma_n^2-sigma_(n-1)^2=w+(beta-1)*sigma_(n-1)^2+alpha*u_(n-1)^2
: 然后,算出u_(n-1)^2的mean和s.d.
: 再令deltaV=sigma_n^2-sigma_(n-1)^2, V=sigma_(n-1)^2
: Since a= 1-\alpha-\beta V_L=w/(1-\alpha-\beta)
| h*******n
发帖数: 24 | 6 又要type公式...郁闷....
1. 如上次提到, deltaV = sigma_n^2-sigma_(n-1)^2, 代入即有deltaV=a*(V_L-V)+
xi*epsilon*V
u_{n-1}^2 确实不是 std normal dist. 再如上次提到, 要求出mean和S.D.,于是有
u_(n-1)^2=sigma_(n-1)^2+sqrt(2)*sigma_(n-1)^2*epsilon
2. how can we add delta_t?
答:直接ADD! 得 deltaV=a*(V_L-V)*delta_t+xi*epsilon*V*sqrt(delta_t)
a
【在 i*****l 的大作中提到】
: Thank you so much for your detailed answer.
: Yes, that is the idea. But I have 2 questions:
: 1. How can you get deltaV=a*(V_L-V)+ xi*epsilon*V?
: u_{n-1}^2 is not std normal dist. any more.
: 2. how can we add delta_t in the above equation?
: With all due respect, this solution, which is also similar to mine, is not a
: mathematical derivation.
:
: normal
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