csi bond valuation handbook · bond valuation:csi provides valuations over thirty-three thousand...
TRANSCRIPT
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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
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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.
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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.
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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
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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.
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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
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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:
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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)
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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.
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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
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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
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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
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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.
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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
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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)
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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
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Contact Us
For authorization and cooperation on CSI bond valuation products, please contact:
Marketing:Mr. Zhi, +86-21-50186582, [email protected]
General Business:Ms. Ma, +86-21-50182732, [email protected]
Technology:Mr. Yang, +86-21-50186519, [email protected]
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