2018

债券估值手册

CSI BOND VALUATION HANDBOOK

2

Contents

About CSI ........................................................................................................................... 3

Introducing CSI Bond Valuation ........................................................................................ 3

CSI Bond Valuation Timeline .................................................................................... 3

Bond Valuation and Yield Curves Family ................................................................. 4

Valuation Products Delivery Channels ...................................................................... 5

The Applications of CSI Bond Valuation ........................................................................... 5

The Design of CSI Yield Curves ........................................................................................ 6

The Definitions of Yield Curves ................................................................................ 6

The Principle of Yield Curve Constructions .............................................................. 7

Constructing Yield Curves Using Bayesian Method ............................................... 10

Efficiency of Bayesian Method ................................................................................ 10

The Principle of Bond Valuation ...................................................................................... 12

The Valuation Process .............................................................................................. 12

CSI Bond Valuation Elements .......................................................................................... 16

3

About CSI

As a joint venture between the Shanghai Stock Exchanges and the Shenzhen Stock

Exchange, the China Securities Index Company Limited (CSI) is a professional

business entity specializing in the creation and management of indices and

index-related services.

CSI is dedicated to serving the capital market and promoting financial innovation

relying on the information and technical advantages of the two exchanges. Focusing

on the series of CSI indices, exchange indices and customized indices, CSI is

becoming the leading index provider in China and in Asia Pacific.

Introducing CSI Bond Valuation

CSI Bond Valuation Timeline

China Securities Index Company Limited (CSI) provides bond valuation services to

domestic institutional investors since 2006. CSI has successfully established a series

of bond valuation related products which include CSI bond valuations, CSI yield

curve family, CSI bond Indices and CSI implied ratings. By successive innovations on

product managements, CSI targests to provide broader and more classified bond

valuation products which to increase the calculation volumn of both yield cuves and

bonds.

4

Bond Valuation and Yield Curves Family

Bond Valuation：CSI provides valuations over thirty-three thousand bonds

which have covered the entire Inter-bank and exchange bond markets on

each Shanghai Stock Exchange trading day (2017). The underlying bonds of

valuation including Treasury bills, Local government bonds, Policy financial

bonds, Commercial banks bonds, Interbank deposits, Commercial papers,

Mid-term notes, Private placement notes/bonds, Corporate bonds, Enterprise

bonds, Asset-backed securities, preferred stocks, Exchangeable bonds,

Convertible bonds, Perpetural bonds.

Yield curve family： The yield curves family of CSI can be classified into

three categories: yield-to-maturity curves, spot-rate curves and forward-rate

curves, each category has thirty-three curves at the present. CSI provides

yield curves for both interest-rate bonds and credit bonds, and these yield

curves can be subdivided and distinguished by bond types and credit rates.

5

Valuation Products Delivery Channels

Delivery time and frequency：CSI delievers bond valuations and yield curves

at 16:30 GMT+8 on each Shanghai Stock Exchange trading day.

Direct delivery channels：Direct data transfer to Shanghai Stock Exchange via

satellite, and via CSI FTP service platform.

Indirct delivery channel：Domistic and international vendors.

The Applications of CSI Bond Valuation

The CSI Bond Valuation products include CSI bond valuations, CSI yield curve

family, CSI bond Indices and CSI implied ratings which has widely implied by

institutional investors and gorvenmental institutions on risk managements and

benchmarks of trade and research. At present, the main applications of CSI Bond

Valuation include fund accountings, index calculations, Treasury Pre-issue

calculations, Exchange Quoted-price Repos, Exchange Tri-party Repos, Collateralised

6

Repos and to be supervision benchmarks.

The Design of CSI Yield Curves

The Definitions of Yield Curves

As the benchmarks of bond yields, CSI yield curve family has full coverages on

various bond types and credit rating, and can be classified by different interest types

such as yield to maturity, spot rate and forward rate.

7

The Principle of Yield Curve Constructions

In order to constract yield curves, the China Securities Index Company Limited (CSI)

employs Bayesian smoothing spline model. The main users of smoothing spline

model are the central banks of United States, Japan, and United Kindom, while CSI

also uses this type of model at present.

Theoretical Basis of Yield Curves Constracting

Yield curve constracting is the process of fitting a smooth continuous curve

based on the trading data (Graph 2.1), which is visible, rational and discrete

distributed in different terms, on the market. Yield curve constracting could be

considered as a nonparametric regression problem:

iii tfy )( , ),0(~ 0 Ni

where iy is the yield of i th point, ni ,,1 ; it is the time to maturity of i

th point; )(tf is the smooth function to be estimated; error term i are

independent random variables.

Graph 2.1 Example of Trading Data

The most commonly used yield curve models can be divided into three categories：

Nelson-Siegel/Svensson Model

Parametric model: the main users are most of the central banks in Europe

8

except United Kindom.

Graph 2.2 Example of Yield Curve by Using NSS Model

Interpolation Model

Interpolation Model：The main representative is the Hermite interpolation

model, of which the main users are U.S. Department of the Treasury and

China Central Depository & Clearing Co., Ltd.

Graph 2.3 Example of Yield Curve by Using Hermite Interpolation Model

Spline Model

Smoothing Spline Model：(Also known as smoothing spline estimate) it is a

nonparametric model, and its principle is to find the solution to the least

squares problem with the penalty term (Penalized Least Squares) in the

following formula:

9

n

i

p

iif

dttftfy1

2)(2 )]([)]([min

Where is called smoothing parameter, which is the key parameter to

control the trade-off between fidelity to the data and smoothness of the

function estimate in curve fitting. When 2p , the function )(tf which

minimizes the formula above is called cubic smoothing spline estimate,

which is the most widely used smoothing spline estimate.

Advantages and Disadvantages of Smoothing Spline Model

The smoothing spline model is a nonparametric model without assumed

parameters for objective functions, which provides the model with more

flexibility.

The smoothing spline model relies on the data, which ensures the

objectivity and fairness of the model.

By appropriate selection of smoothing parameters, the model has good

balance between goodness of fit and smoothness.

Graph 2.4 Example of Yield Curve by Using Smoothing Spline Model（ =0.016）

10

Constructing Yield Curves Using Bayesian Method

The characteristic of ‘prior distribution + sample information posterior

distribution’ in Bayesian method conforms to the general cognitive processes. The

assumptions could be modified by constantly updating the sample parameters,

hence the posterior distribution to reflect all the current informations on unknown

parameters. The inferential statistics of posterior distribution is approachable but

require an amount of works.

Application of Bayesian Method in Smoothing Spline

The choice of depends on the morphological characterization of

specific observations. The frequentists think is a specific value. On

the contrary, the Bayesians think itself as a random value that obeys

a certain distribution. According to the prior experiences, we assume

that it obeys a certain distribution (prior distribution), we then calculate

this posterior distribution by using Bayes' theorem.

The Baysians do not limit the specific value of , but choose its prior

distribution based on Bayesian theory and prior information.

We use Monte Carlo algorithm for parameter estimations. In order to

obtain the yield curve, we calculate the Bayes estimator for each

parameter by using the posterior mean.

Efficiency of Bayesian Method

Objectivity

Bayesian method reduces the subjective factors involved in the traditional spline

models, for instance, it avoids the subjective choice of parameters, such as the

forms of spline function, interval numbers and node positions. Bayesian method

also improves the efficiency and robustness of smooth parameter estimation,

enhances the stability of numerical calculations.

11

Fairness

The yield curve based on Bayesian method ensures all the sample informations to

reflect the real-time changes on the market with broader coverages.

Stability

Bayesian method enhances the stability and consistency of the model by curve

fitting and parameter estimation.

Scientificity and Efficiency

The computational procedure of Bayesian method is simple and practicable with

high computational efficiency; it helps with the constructions of high-frequency

real-time yield curves and real-time bond valuation.

（a）9:30-10:00 （b）10:00-10:30

（c）11:30-12:00 （d）16:00-16:30

Graph 2.5 Yield curves based on Baysian Method on several time periods

12

The Principle of Bond Valuation

According to the principle of financial pricing model, bond pricing employs the

discounted cash flow model.

（1）

Index:

P：Bond price

：Cash flow in ith

coupon period

y：Yield to maturity, equals to the value of bond allocated implied rating’s yield +

Spread

f：Frequency of yearly coupon payments

d：Remaining days in the present coupon period

TS：Actual days in the present coupon period

The Valuation Process

The basic process of bond valuation is to determine the value of each parameter

on the right-hand side of the formula (1).

The Determination of Cash Flow（Numerator Part）

The cash flow of bond is determined by its terms of issue. There are several types

of bond with different cash flow structures: Vanilla bond, Redemptional bond,

Floating-rate bond, Adjustable-rate bond and bond with irregular cash flows

which mainly exist in Asset-backed securities and can be valued by its provisions.

Vanilla bond

The cash flow of Vanilla bond on each coupon period equals to the coupon

rate mutilplying by face value then deviding by the number of coupon

13

periods per year, therefore formula (1) could be modified to:

（2）

Index:

：Coupon yield

：Face value

Redemptional bond

For a redemptional bond, the cash flow is calculated based on the remaining

outstanding bond principal in the present coupon period; therefore formula (2)

could be modified to:

（3）

Index:

: Proportion of outstanding bond principal in the present coupon period

: Proportion of principal to be paid in the end of the present coupon period

: Proportion of outstanding bond principal in ith

coupon period

: Proportion of principal to be paid in the end ith

i Th coupon period

Adjustable-rate Bond

Adjustable coupon rate usually exists as the collateral term to the bond with

imbedded options. Its cash flow could be determined by the coupon rate in

each period, therefore formula (3) could be modified to:

（4）

Index:

：Coupon rate in the present coupon period

：Coupon rate in ith

coupon period

14

Floating-rate Bond

The floating-rate bond could be considered as a special case of

adjustable-rate bonds. The benchmark interest rate for floating-rate bond is

updated and replaced by its latest value on each valuation day, therefore

formula (4) could be modified to:

（ ）

Index:

: benchmark interest rate in the present coupon period

：fixed spread

：benchmark interest rate on valuation date

The Determination of Discount Rate（Denominator Part）

The valuation applies the yield to maturity. For the bond with call provision, we

determine the maturity and exercise period by using spot rates in addition to the yield

to maturity. The yield to maturity of the bond equals to the sum of the value of bond

allocated implied rating’s yield and a spread:

where equals to the value of allocated bond implied rating’s yield on the

valuation day, and the spread remains unchanged to the last trading day or to be

altered by the yield to maturity of the bond that newly listed in the primary

market and/or traded in the secondary market on the day.

Spread for newly listed bond

For a newly listed bond, its spread could be determined based on the coupon

yield and the yield of trading on secoundary market.

15

Spread for traded bond

For the bond that traded with a reasonable yield and satisfy the trading data

validation criteria, the spread could then be determined by this corresponding

trade.

Trading data validation:

Trading data sources include brokers, interbank market and stock

exchanges. The factors of trading data validation include the transaction

price, the continuity and the volatility of the quotes, and the size of

trading volume.

Credibility levels:

Trading data can be divided into stage according to the level of

activeness: extremely active, active and reasonable which reflects the

degrees of credibility of trade.

Spread for Non-active Bond

For the bond without secondary prices, the spread remains unchanged to

the last trading day.

Puttable Bond Valuation

The key of puttable bond valuation is to determine whether to exercise the put

option. Based on the hypothesis of the market is being rational, CSI determines

whether to exercise the option by comparing the valuation of the bond and the

trading data

extremely active

active reasonable

16

put price, assuming that investors choose not to sell back the bond on the exercise

date.

（6）

Index:

：numbers of coupon payments until the exercise date

：numbers of coupon payments between the exercise date and the maturity date

：period between the exercise date and the th payment date

：forward rates during the period between the exercise date and the th payment

date

CSI Bond Valuation Elements

CSI bond valuation includes:

Full price, Clean price, Yield to worst, Yield to maturity, Macaulay duration,

modified duration, convexity, accrued interest and the other valuation elements.

Macaulay Duration

（7）

17

Modified Duration

（8）

Convexity

（9）

Yield to Maturity

Yield to maturity (YTM) is the total return anticipated on a bond if the bond

is held until it matures.

Yield to Worst

The yield to worst (YTW) is the lowest potential yield that can be received

on a bond without the issuer actually defaulting.

Dirty Price, Clean Price and Accrued Interest

Dirty Price = Clean Price + Accrued Interest

18

Contact Us

For authorization and cooperation on CSI bond valuation products, please contact:

Marketing：Mr. Zhi, +86-21-50186582, lzhi@sse.com.cn

General Business：Ms. Ma, +86-21-50182732, xma@sse.com.cn

Technology：Mr. Yang, +86-21-50186519, xiaoyyang@sse.com.cn

Subscribe us on Wechat: CSIBOND