关于期货动态策略的问题

如下，第三张PPT的表格看不懂~~~~求讲解。其实整个故事我就没有太看明白。

B t, T <1, 是discount rate

苇萱 发表于 2013-10-1 23:05
many thx for your reply.

我知道期货账户每天都要结算一次，如果亏损就需要追加保证maintenance marg ...

OK, perhaps I mis-expressed it.

put it in this way.

If you long a forward=borrowing money+buy a spot. In that case, you position is fully covered. The interest rate you borrowing money is fixed at the time you borrow, so that there is no interest risk.

but if you have a future. you will have a interest risk. Since you will receive a cash flow every day, because the interest is stochastic which means you don't know the future spot rate at time 0 (e.g. at time 0, you don't know B(1,2)), in that case, you have to replicate the borrowing cost with a serious of bond. Not fix a interest rate like forward B(0,T) but B(0,1),B(1,2)...(money market account), that is replicate the borrowing cost day by day.
At last, for forward, the price is ST/B(0,T) but for future it is ST/[B(0,1)B(1,2)B(2,3)...B(T-1,T)].

So this example is actually telling you what's difference between the forward price and futures price.

so that is basically what is happening.

best,

It is just an replication of futures contract under stochastic interest rate.

You know how to replicate the cash flow of a  forward contract right?  

But the future is a little different. The difference between forward and future is future has a mark to market mechanism which means it have a series of cash flows. In this case, we have to replicate the future every day which means we have to construct a portfolio with a certain number of share of Stocks and Bonds so that we can replicate everyday's cash flow not just maturity(forward just need to replicate maturity)

So that is basically what these three slides are talking about. They teach you how how many you need to buy and what are the corresponding cash flow every day.

best,

Chemist_MZ 发表于 2013-10-1 22:51
It is just an replication of futures contract under stochastic interest rate.

You know how to rep ...

many thx for your reply.

我知道期货账户每天都要结算一次，如果亏损就需要追加保证maintenance margin。但是我不明白为什么要construct a portfolio with stocks and bonds。您能再说具体一点吗？真是非常感谢您的回复，我纠结这个问题纠结好久了。

Chemist_MZ 发表于 2013-10-1 23:28
OK, perhaps I mis-expressed it.

put it in this way.

谢谢了~~我遇到大牛了啊~~我再仔细想想，如果不懂再来问您~

苇萱 发表于 2013-10-1 23:05
many thx for your reply.

我知道期货账户每天都要结算一次，如果亏损就需要追加保证maintenance marg ...

For more clear explanation.

Your purpose is to get a unit of ST at time T

You can long a forward contract and borrow the money at B(0,T), so at last you actually get ST for ST/B(0,T).

But we can not naively long a future correct? We don't know the future interest rate since we may receive some cash flow before the settlement, if we deposit these cashes this may cover some cost for us to buy ST.

So what we do is following the strategy in the table. The net position (profit) ST/[B(0,1)B(1,2)...B(T-1,T)] which is the futures price at time 0 is exactly the amount of money we need to pay to buy an ST at time T. Because we can replicate the cash flow at T, this means that the cash flow is also replicated on the path (1,2,3,...T-1) so this is the basic meaning of the three slides.

To summarize, the logic is, to buy a unit of ST at time T, you must have ST/[B(0,1)B(1,2)...B(T-1,T)] of cash on hand at time T. So your strategy is following the table in the slide. It can exactly generate ST/[B(0,1)B(1,2)...B(T-1,T)] at time T which is just enough to buy a unit of ST.


My previous explanation does not catch the point. It just tell you the difference between forward and future replication.
Hope this one is clearer.

best,

ding...........

Chemist_MZ 发表于 2013-10-2 00:00
For more clear explanation.

Your purpose is to get a unit of ST at time T

非常感谢~感觉之前的很多理解都是错误的~~~大牛啊~~~

Chemist_MZ 发表于 2013-10-1 22:11
OK, perhaps I mis-expressed it.

put it in this way.

您给我说的这些，我的教材上都没有写啊，可能是因为我没有学过任何衍生品的知识，就直接开始学定价……请问有没有什么推荐的资料啊，多谢。

苇萱 发表于 2013-10-2 00:46
您给我说的这些，我的教材上都没有写啊，可能是因为我没有学过任何衍生品的知识，就直接开始学定价……请 ...

I know, most of the text books will not say this. Even not included in Hull's book.

I learn it from my advisor.

But I can give you a tip that will help you to think the things in a different way.

The main function of a derivative (especially some derivative with linear payoff) is to operate the cash flow. This means that whenever you have a derivative on hand, it is not a derivative but a series of future and spot cash flows. In this case, if you can exactly replicate these cash flows with existing assets, you actually manually "create" a derivative by yourself and of cause the price of this derivative is the summation of the prices of the assets you use to replicate it.

The main part lies in your skill to decompose the derivative.

And a by-product is that with derivative and by manipulating the cash flows, you can do many things that previously unable to do. For example, long a forward=borrowing money+buying a spot.

if you modify this equation:

borrowing money=long a forward+shorting a spot. Short a spot will give you some cash right now and long a forward will lock the price at maturity. So at maturity, the forward is settled, you buy back the asset and then close your short position. The money you pay is just the interest rate. In this case, you borrow some money without go to the bank and "borrow" it.

Analyzing cash flow and replicate these cash flow is very important in derivative both pricing and risk management. So try to think it in this way.

best,