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金融计算代写-BUFN 732

时间：2021-03-31

Prof. Haluk Unal Fixed Income Analysis 1

Flat - Full Price

BUFN 732 Fixed Income Analysis

Prof. Haluk Unal Fixed Income Analysis 2

Bond price calculation

In the following set up for the bond price:

P is calculated as if the date of the cash exchange for the bond is t=0. In other words, we find the

price of the bond as the PV of future cash flows as of t=0.

However, the settlement date, the time when cash is exchanged for the bond, may not be at t = 0.

The settlement date can be some time between t = 0 and t = 1.

This real-life complication has implication for valuation.

P

t=0

C

1

C

2

C

3

C+F

4

Prof. Haluk Unal Fixed Income Analysis 3

An example for bond price calculation

Consider the example,

This 5% bond makes coupon payments semiannually on June 15 and December 15. Suppose its YTM

is 4% and this bond is purchased on June 15 (excluding the June coupon), but will settle on August

21. At that time, four coupon payments remain for the rest of the bond.

June 15 Dec 15 June 15 Dec 15 June 15

$25 $25 $25 $25+$1000

Prof. Haluk Unal Fixed Income Analysis 4

An example for bond price calculation (cont’d)

If the bond were to be exchanged for cash on June 15, the valuation would have been:

However, the cash settlement is on August 21 (67 days after June 15):

June 15 June 15

25+1000

Dec 15Dec 15June 15

August 21

183 days

67 days

P =

25

1.02

+

25

1.02 2

+

25

1.02 3

+

25 + 1000

1.02 4

= $1019.04

Prof. Haluk Unal Fixed Income Analysis 5

An example for bond price calculation (cont’d)

The value at settlement date ( the full price of the bond) is:

Note that, this full price includes accrued interest between last coupon and settlement date. To

figure out this accrued interest:

In other words, the seller is entitled to this $9.15 interest because he/she has not received the cash till August 21.

Full Price = 1019.04 ∗ 1.02 67

/183 = $1026.46

Accrued Interest = $25 ∗ (

67

183

) = $9.15

Prof. Haluk Unal Fixed Income Analysis 6

Calculation for full price

Hence, the full price has two components:

Full Price = Accrued Interest + Flat Price.

Flat Price = Full Price - Accrued Interest = 1026.46 - 9.15 =$1017.31

Flat price is also called “clean” price meaning value that is free of accrued interest; Full price is also

called “dirty” price because it includes elements of accrued interest.

1019.04

1026.46 = Full Price.

Accrued Int

= 9.15

25 25 25 25+1000

(This price includes the accrued interest on principal and the coupon.)

1017.31

Flat price

9.15

Accrued Interest on coupon

Prof. Haluk Unal Fixed Income Analysis 7

Calculation for accrued interest

In calculating accrued interest, note that we used actual number days between coupon

payments (183 days) and the actual number of days between the last coupon date and

the settlement date (67 days).

This actual/actual method is used most often with government bonds.

Prof. Haluk Unal Fixed Income Analysis 8

Calculation for accrued interest (cont’d)

There is another method that assumes there are 30 days in each month and 360 days in a year. In this

method:

June 15 Dec 15

25 25 25 25+1000

August 21

August 15

2*30 =

60 days

6 days

66 days

180 days

Accrued interest = 25*(66/180) = $9.166

*Note that under the 30/360 method the accrued

interest is slightly more.

Prof. Haluk Unal Fixed Income Analysis 9

Quotation conventions

If the bond price is quoted clean price (flat price), this is not the price what you actually pay to buy

the bond. You have to include the accrued interest in the price you pay, which is the dirty price (full

price).

Corporate and municipal bond issuers assume a 30/360 method. However, government bonds use

actual/actual method.

When the price of coupon bonds are quoted, they are either quoted at a full price or flat price.

Bonds may trade at flat price if the bond settles on the same date as interest paid, so no accrued

interest exist. Alternatively, bonds in default may trade at flat price.

Flat - Full Price

BUFN 732 Fixed Income Analysis

Prof. Haluk Unal Fixed Income Analysis 2

Bond price calculation

In the following set up for the bond price:

P is calculated as if the date of the cash exchange for the bond is t=0. In other words, we find the

price of the bond as the PV of future cash flows as of t=0.

However, the settlement date, the time when cash is exchanged for the bond, may not be at t = 0.

The settlement date can be some time between t = 0 and t = 1.

This real-life complication has implication for valuation.

P

t=0

C

1

C

2

C

3

C+F

4

Prof. Haluk Unal Fixed Income Analysis 3

An example for bond price calculation

Consider the example,

This 5% bond makes coupon payments semiannually on June 15 and December 15. Suppose its YTM

is 4% and this bond is purchased on June 15 (excluding the June coupon), but will settle on August

21. At that time, four coupon payments remain for the rest of the bond.

June 15 Dec 15 June 15 Dec 15 June 15

$25 $25 $25 $25+$1000

Prof. Haluk Unal Fixed Income Analysis 4

An example for bond price calculation (cont’d)

If the bond were to be exchanged for cash on June 15, the valuation would have been:

However, the cash settlement is on August 21 (67 days after June 15):

June 15 June 15

25+1000

Dec 15Dec 15June 15

August 21

183 days

67 days

P =

25

1.02

+

25

1.02 2

+

25

1.02 3

+

25 + 1000

1.02 4

= $1019.04

Prof. Haluk Unal Fixed Income Analysis 5

An example for bond price calculation (cont’d)

The value at settlement date ( the full price of the bond) is:

Note that, this full price includes accrued interest between last coupon and settlement date. To

figure out this accrued interest:

In other words, the seller is entitled to this $9.15 interest because he/she has not received the cash till August 21.

Full Price = 1019.04 ∗ 1.02 67

/183 = $1026.46

Accrued Interest = $25 ∗ (

67

183

) = $9.15

Prof. Haluk Unal Fixed Income Analysis 6

Calculation for full price

Hence, the full price has two components:

Full Price = Accrued Interest + Flat Price.

Flat Price = Full Price - Accrued Interest = 1026.46 - 9.15 =$1017.31

Flat price is also called “clean” price meaning value that is free of accrued interest; Full price is also

called “dirty” price because it includes elements of accrued interest.

1019.04

1026.46 = Full Price.

Accrued Int

= 9.15

25 25 25 25+1000

(This price includes the accrued interest on principal and the coupon.)

1017.31

Flat price

9.15

Accrued Interest on coupon

Prof. Haluk Unal Fixed Income Analysis 7

Calculation for accrued interest

In calculating accrued interest, note that we used actual number days between coupon

payments (183 days) and the actual number of days between the last coupon date and

the settlement date (67 days).

This actual/actual method is used most often with government bonds.

Prof. Haluk Unal Fixed Income Analysis 8

Calculation for accrued interest (cont’d)

There is another method that assumes there are 30 days in each month and 360 days in a year. In this

method:

June 15 Dec 15

25 25 25 25+1000

August 21

August 15

2*30 =

60 days

6 days

66 days

180 days

Accrued interest = 25*(66/180) = $9.166

*Note that under the 30/360 method the accrued

interest is slightly more.

Prof. Haluk Unal Fixed Income Analysis 9

Quotation conventions

If the bond price is quoted clean price (flat price), this is not the price what you actually pay to buy

the bond. You have to include the accrued interest in the price you pay, which is the dirty price (full

price).

Corporate and municipal bond issuers assume a 30/360 method. However, government bonds use

actual/actual method.

When the price of coupon bonds are quoted, they are either quoted at a full price or flat price.

Bonds may trade at flat price if the bond settles on the same date as interest paid, so no accrued

interest exist. Alternatively, bonds in default may trade at flat price.