Term Structure of Interest Rate
Term Structure of Interest Rate. Candidate number 25909
Section 2
In this section, I will introduce some essential components about term structure, explain the IS/LM model to reveal the relation between term structure and GDP growth and lastly bring in some empirical evidence to support this relation.
2.1 Some basic terminologies and equations
Bond, being one of the most popular financial products, is one example of firm’s and nation’s lending and borrowing. There are two ways a bond delivers its return. (Please note that when comparing the yield of different bonds, only the terms to maturity vary. All other characteristics are identical.)
The first way is to offer a coupon every period and the principle along with a coupon when the bond matures. Face value is denoted by D. coupon payment by C, maturity by N, price by P, yield by Y. The log of each variable is expressed in lower case. Now, we can calculate the price of bond with a yearly coupon payment by [1]:
And if we assume the payment is in continuous stream, the time difference is dt and the coupon payment is there for Cdt. Then the price equation is [1]:
The second way is to only offer its face value on a specified date, no coupon payment before it matures. This type is called zero-coupon bond and the price of it is just [2]:
Again, if we rearrange and show it in a continuous form [2]: ; (Please note that in the above three equations, Professor John H. Cochrane considers Y(N)
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Term Structure of Interest Rate. Candidate number 25909
and y(N) as one plus the yield to maturity (YTM), namely Y(N)=1+YTM and log(Y(N))=log(1+YTM)=y(N).)
In a more widely expressed form, the yield of a zero-coupon bond, for purchasing a bond at its current price and holding it till maturity at time N to receive £1, is the following:
Since
Another vital rate for the term structure is the forward rate, maturity and N’ is the years of holding. For instance,
, where N is the year of means
Section 2
In this section, I will introduce some essential components about term structure, explain the IS/LM model to reveal the relation between term structure and GDP growth and lastly bring in some empirical evidence to support this relation.
2.1 Some basic terminologies and equations
Bond, being one of the most popular financial products, is one example of firm’s and nation’s lending and borrowing. There are two ways a bond delivers its return. (Please note that when comparing the yield of different bonds, only the terms to maturity vary. All other characteristics are identical.)
The first way is to offer a coupon every period and the principle along with a coupon when the bond matures. Face value is denoted by D. coupon payment by C, maturity by N, price by P, yield by Y. The log of each variable is expressed in lower case. Now, we can calculate the price of bond with a yearly coupon payment by [1]:
And if we assume the payment is in continuous stream, the time difference is dt and the coupon payment is there for Cdt. Then the price equation is [1]:
The second way is to only offer its face value on a specified date, no coupon payment before it matures. This type is called zero-coupon bond and the price of it is just [2]:
Again, if we rearrange and show it in a continuous form [2]: ; (Please note that in the above three equations, Professor John H. Cochrane considers Y(N)
1 / 19
Term Structure of Interest Rate. Candidate number 25909
and y(N) as one plus the yield to maturity (YTM), namely Y(N)=1+YTM and log(Y(N))=log(1+YTM)=y(N).)
In a more widely expressed form, the yield of a zero-coupon bond, for purchasing a bond at its current price and holding it till maturity at time N to receive £1, is the following:
Since
Another vital rate for the term structure is the forward rate, maturity and N’ is the years of holding. For instance,
, where N is the year of means