[toc]
background
interest rate is probably the most important part in finance , maybe even more important than none-arbitradge . because interest rate means the money in different time means differently .
if you still ask why to every answer , after 5 or 6 times , you will come to an area , where there is a same question , and that question is probably the main idea of that subject .
in physics , you will meet dirac equation , they will tell you every thing is about to find a sammitry . in finance , it will be how to balance different resource from different time . the relation ship between different time is interest rate .
i will add some more personal understanding at the end of this essay , now let’s start from a more specific spot : bonds.
theory
calculate from bonds
theoritically , the goveronment or central bank will offer long-term bonds or , which in fact is a serious of cashalow , for example :
pay you $10 every year , at the tenth year , pay you $110 .
this kind of bond may have a price today $p$, if we mark the $ in time t as $Z_t$ , the cash flow at time t as $c_t$ simply we have :
[p*Z_0 = \sum_{t_i}c_{ti}Z_{t_i}]
mormally , we have a series of bond , that means if we use index j to denote No.j bond , we have :
[p_jZ_0 = \sum_{t_i} c_{t_i,j}Z_{t_i}]
which is a linear equation , if the number of j is less than the number of $t_i$ , there will be infinit solution , if the number of j is larger than the ti , that would mean the bonds are linear deependent , or there would be arbitradge oppotunity . by defination , $ at same time chan exchange with each other .
than there comes a question : what if i want to exchange today’s money with some time isn’t exist in the time series ?
we will do some interpolation between the ${Z_{t_i}}$ , for some different reason , people will choose different interpolation method , but i think the interpolation details is decided by some statastic theory , and it also depend’s on what is the interest rate you are calculating .
if you are calculating the cost of borrowing money for your self , you should considering calculate a higher one , if you are calculating your profit for stoving , you should considering a lower one .
calculate from the libor
in fact , except the bonds market , there is another market called money market , where between bank they calculate lobar everyday , that is a flout market .
technical details
the theory is really easy but the details is not , so i must give some realistic example to illustrate what a bond is :
in fact , a bond is really easy , you can simply say how much there will be in which day , but in fact people follow a series of rules to define a bond , because of my ugly homeworrk , i’ll show these details with the package : quantlib for python , this is a package written by c++ , but can be import by python , honestly speaking , idon’t think this package outstanding at all . but i have to use it , because of my th=eacher .
LI YUSU
i'm LI YUSU , a master student in NUS right now , i'm curious about all the theory people had developed , i'll shsare some of my understanding about them.
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