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BUFN 732 Fixed Income Analysis
Creation date：2024-04-07 16:55:47
Belonging category：金融Finance
Fixed Income Analysis

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Flat - Full Price
BUFN 732 Fixed Income Analysis

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.

4

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

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

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

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.

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.
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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