z****i
发帖数: 406 | 1 是为什么的呀，有数学的证明而不只是解释么？
另外，这个结论是用来证futures RATE is martingale under risk neutral measure
的吧？又是怎么证的呢？ |
w*****e
发帖数: 197 | 2 Just treat future process as a stock with a special dividend process. Then
it is not hard to see why it is martingale. But for interest rate future
like EuroDollar, I am not sure what you are saying is true in general.
Remember, anything can be a martingale, as long as you are willing to work
with a particular kind of risk neutral measure.
On the other hand, future RATE is a rather hard thing to model. You always
start with some kind of framework that works with short rate or forward rate
. I am not sure what you are referring to here. |
t***l
发帖数: 3644 | 3 Shreve的两册书上有证明。
measure
【在 z****i 的大作中提到】
: 是为什么的呀，有数学的证明而不只是解释么？
: 另外，这个结论是用来证futures RATE is martingale under risk neutral measure
: 的吧？又是怎么证的呢？
|
z****i
发帖数: 406 | 4 Thanks a lot.
Just took a look at Shreve's book. It doesn't seem to be quite obvious to
show the martingale property though.
For ED futures, let F(t; T1, T2) be the time-t future rate (simply
compounded), from T1 to T2.
Let L(t; T1, T2) be the forward Libor rate.
Then we have F(t; T1, T2) is a martingale under risk-neutral measure, so is
the ED futures price of course.
Moreover, F(t; T1, T2) is the expectation of L(t; T1, T2) under risk-neutral
measure.
Future rates are quoted directly from market, and resettled day to day.
Models are needed to find the convexity adjustment to calculate the forward
rates.
Please let me know if I'm saying something nonsense.
rate
【在 w*****e 的大作中提到】
: Just treat future process as a stock with a special dividend process. Then
: it is not hard to see why it is martingale. But for interest rate future
: like EuroDollar, I am not sure what you are saying is true in general.
: Remember, anything can be a martingale, as long as you are willing to work
: with a particular kind of risk neutral measure.
: On the other hand, future RATE is a rather hard thing to model. You always
: start with some kind of framework that works with short rate or forward rate
: . I am not sure what you are referring to here.
|
w**********y
发帖数: 1691 | 5 我困惑了..我怎么记得discounted price of any asset is martingale under risk
neutral measure啊?
不是么? |
M********t
发帖数: 163 | 6 我记得我的NOTES上有，回头给你查查。
measure
【在 z****i 的大作中提到】
: 是为什么的呀，有数学的证明而不只是解释么？
: 另外，这个结论是用来证futures RATE is martingale under risk neutral measure
: 的吧？又是怎么证的呢？
|
m*******r
发帖数: 98 | 7 You can treat future as a one period contract.
The value at t = 0 is zero.
The payoff at t = 1 is F_1 - F_0.
0 = E(F_1 - F_0) / (1 + r)
E(F_1|F_0) = F_0
measure
【在 z****i 的大作中提到】
: 是为什么的呀，有数学的证明而不只是解释么？
: 另外，这个结论是用来证futures RATE is martingale under risk neutral measure
: 的吧？又是怎么证的呢？
|
m*******r
发帖数: 98 | 8
Future price is the contract price, not the asset price.
【在 w**********y 的大作中提到】
: 我困惑了..我怎么记得discounted price of any asset is martingale under risk
: neutral measure啊?
: 不是么?
|
m*******r
发帖数: 98 | 9
Future price is the contract price, not the asset price.
【在 w**********y 的大作中提到】
: 我困惑了..我怎么记得discounted price of any asset is martingale under risk
: neutral measure啊?
: 不是么?
|
w*********m
发帖数: 196 | 10 shreve第二册第6章最后讲的，主要是定义的问题 |
n*******e
发帖数: 107 | 11 future contract也是一种asset
rn measure下无yield的asset都应该只有risk free drift
可是这个结论一点都没有意思
因为future的underlying基本都有yield的：股票有divident，commodity有
convenience yidle，这些yield才把futures price搞复杂的
【在 m*******r 的大作中提到】
:
: Future price is the contract price, not the asset price.
|
