Pricing Credit Risk of Asset-Backed Securitization Bonds in Singapore
TIEN FOO SING*, SEOW ENG ONG, GANG-ZHI FAN
Department of Real Estate, School of Design & Environment,
National University of Singapore,
4 Architecture Drive, Singapore 117566
*rststf@nus.edu.sg
and
KIAN GUAN LIM
School of Business, Singapore Management University, Singapore
Revised: June 17, 2004
Abstract
Asset-backed securitization (ABS) is a creative arrangement to raise funds through the
issuance of marketable securities backed by predictable future cash flows from revenueproducing assets. This paper proposes two pricing models: structural model and intensity
model, to value credit spreads on Singapore ABS bonds. Sensitivity analyses were
conducted on the ABS credit spreads by varying the values of the key input variables
within a plausible range. The property price volatility and its correlations with risk-less
interest rates have been shown to have positive effects on the ABS credit spreads.
However, when the market volatility is extremely high, the credit spreads decrease with
an increase in the time to maturity. The positive effects of the property price volatility
were significantly reduced when credit enhancements were added to the ABS bonds, and
the credit risks associated with the correlation variable were fully eliminated in the credit
enhanced ABS bonds. The rate of loss recovery in the event of default also has significant
impact on the credit risks of the ABS bonds. ABS bonds backed by physical property will
likely to have high recovery rates thus reducing the credit risks vis-à-vis noncollateralized bonds.
Keywords: Asset Backed Securitization; credit risk; structural model; intensity model
*
We would like to thank National University of Singapore for funding the research project. We
also wish to thank Brent Ambrose, CF Sirmans, anonymous referees and others for their
constructive comments and suggestions on the earlier version of the paper. Errors, if any,
remain the responsibility of the authors.
1
Pricing Credit Risk of Asset-Backed Securitization Bonds in Singapore
1.
Introduction
Asset-backed securitization (ABS) is a creative arrangement to raise funds by issuing
marketable securities backed by future cash flows from revenue-producing assets. In the
Singapore context, the assets consist of real estate assets with regular cash flows. A
special-purpose vehicle (SPV) is set up in the ABS structure, which issues debt securities
to finance the purchase of the real estate assets. After the Asian financial crisis in 1997,
ABS transactions became popular in Singapore. The first securitization deal involved the
sale of Neptune Orient Lines (NOL)1 headquarter office building in 1999. 10-year fixedrate bonds were issued through a special purpose vehicle (SPV) Chenab Investments
Limited, to fund the purchase of the 26-storey building valued at S$185 million. Six other
asset securitization transactions were subsequently concluded in 1999. The total bonds
issued from the seven ABS transactions amounted to S$1.84 billion. Securitization of
S$2billion worth of non-real estate assets was also initiated by the Development Bank of
Singapore (DBS)2, with the first tranche of S$200 million short-term interest bearing
notes launched in June 2000.3 The asset pool comprises loans granted to statutory boards
of Singapore and bonds issued by government-linked companies. The short-term notes
were the first asset backed securitization instrument that was assigned an “A-1” rating by
the Standard and Poor’s, which marks an important milestone in the development of ABS
market in Singapore.
ABS is a relatively new financial innovation in Singapore. As yet, there has been no
academic study on credit risk evaluation on Singapore ABS transactions due largely to
shortage of empirical data given the short history of Singapore ABS. Traditional
valuation methods estimate credit spreads by analyzing ex-post default data using
1
2
3
Founded in 1968, Neptune Orient Lines (NOL) is the largest shipping company listed on the Singapore
Exchange. NOL operates a network of container transportation and logistic services on major
international trade routes.
The Development Bank of Singapore (DBS) listed on the Singapore Exchange is one of the largest
banks in Singapore, in term of market capitalization.
Siow, L.S., “DBS offers retail investors short-term interest notes,” Business Times Singapore, June 1,
2000.
2
empirical credit risk models. The modern derivative theory offers a theoretical approach
to pricing credit risk of defaultable bonds, which include the ABS bonds in this paper.
There are two approaches commonly used to evaluate credit risk of defaultable bonds: a
structural-based (firm value) model and an intensity-based model. In the structural or
firm value approach, default and recovery rates are determined based on the evolution of
the firm value relative to its liability. While in the intensity model, an exogenous default
process is directly modeled as a Poisson process. This study attempts to employ the two
models to separately analyze and value credit risk in the ABS transactions.
The organization of the paper is as follows: Section 2 reviews the relevant literature on
pricing defaultable debt instruments. Section 3 discusses the key security features relating
to the selection and applicability of credit risk quantitative valuation techniques. Section
4 specifies the two comparable approaches proposed to price the credit spreads of ABS
bonds. Sections 5 and 6 evaluate the numerical properties of the credit spreads based on
the proposed models. Section 7 summarizes the results of the investigation and draws
some conclusions.
2.
Valuation of Defaultable Debts
Based on the classical option pricing theory first developed by Black and Scholes (1973)
and Merton (1973), Merton (1974) prices the default risk of defaultable bond as a
European put option on the total value of firm assets. The firm value is assumed to evolve
following a stochastic diffusion process. The defaultable zero-coupon bond is then
modeled as an arbitrage-free portfolio consisting of a long position in an equivalent
Treasury bond and a short position in a put option on the firm value with an exercise
price equal to the bond’s face value. Default occurs when the firm value drops below the
face value of its bond at maturity. Merton’s (1974) model suffers several drawbacks.
Firstly, default risk is independent of interest rate risk and different seniority levels.
Secondly, the possibility of default before debt maturity was excluded. Jones et al (1984)
and Franks and Torous (1989) showed that the empirical credit spreads on corporate
3
bonds were too high to be consistent with those generated from the Merton’s model with
non-stochastic interest rates.
Shimko et al. (1993) make a significant extension to Merton’s model by allowing
stochastic interest rates in the model. The interest rates are assumed to follow the Vasicek
(1977) process, which fits many observed term structures of interest rates. In the Vasicek
process, it is possible to generate negative interest rates. They derived closed-form
solutions for defaultable zero-coupon bonds, and showed that the correlation between the
returns of underlying asset and the interest rate movements plays an important role in
determining the credit spread on bonds. However, their model does not allow default
before debt maturity.
Kim et al. (1993) developed their corporate bond pricing model by defining default as the
time when the firm value first reaches a pre-specified constant default threshold. They
incorporated stochastic interest rates in the model, which are assumed to evolve
following a square-root CIR process (Cox, Ingersoll, and Ross, 1985). When the default
threshold is crossed, default occurs and the firm is assumed to go bankrupt immediately.
Bondholders will then exogenously receive a given amount of riskless bonds upon
default. They showed that the proposed model is able to generate corporate spreads that
match with those observed in practice (also see Nielsen et al., 1993; Longstaff and
Schwartz, 1995; and Briys and de Varenne, 1997). This structural valuation framework of
Kim et al. (1993) will be adopted as the first credit risk model for ABS bonds.
Structural models have, however, some practical limitations. Firstly, it is difficult to
estimate the required input parameters related to the value of the firm. The firm’s assets
are generally not frequently traded in financial markets. The firm value is, therefore, not
directly observed. In our case, the assets are commercial properties. If transactions of
comparable properties are not available in the market, the price movements of these
properties can still be indirectly inferred through relevant property indices published by
relevant authorities. Secondly, structural models do not explicitly account for credit
rating information that reflects the credit quality changes of defaultable corporate bonds.
4
It is important, however, in practice, to incorporate the relevant credit-rating information
into the proposed valuation models.
The intensity model offers an alternative approach, in which rating agencies’ data or
other relevant financial markets series can be incorporated into the valuation process. In
the intensity model, default or bankruptcy is directly treated as an unpredictable event
(i.e. a Poisson process). The probability of a jump from no-default to default in a given
time interval is measured by a hazard rate, which is also called an intensity rate. This
group of credit risk models have been examined in financial literature, which includes
Ramaswamy and Sundaresan (1986), Madan and Unal (1994, 1999), Jarrow and Turnbull
(1995), Duffie and Huang (1996), Schönbucher (1997), Duffie and Singleton (1999) and
others.
In Ramaswamy and Sundaresan (1986) intensity model, they assumed that the
instantaneous default risk premium evolves according to a stochastic CIR process (Cox et
al. 1985). In a risk-adjusted valuation procedure, Duffie and Singleton (1999) show that
risky corporate bonds can be directly priced by discounting promised payments using
risk-adjusted interest rates. In Jarrow and Turnbull (1995) intensity model, default is
governed by a constant-parameter Poisson process that is independent of default-free
interest rates. The payoff is known before default. More recently, Madan and Unal (1999)
proposed a two-factor hazard-rate model. The stochastic hazard rate is specified as a
function of the firm’s asset value and the default-free interest rate, which are driven by
two independent stochastic processes. They showed that the proposed hazard-rate model
generates a rich array of credit-spread shapes that are consistent with those observed in
practice.
3.
Problem Specifications
In a typical ABS deal, an owner of an income-generating property asset sells the asset to
a special purpose vehicle (SPV), which is created specifically to hold the asset in the
securitization process. This process distinguishes a securitization arrangement from the
traditional mortgage-backed or collateralized bond issues (Sing, Ong and Sirmans, 2003).
5
The SPV is usually a shell company with no assets. It will raise funds through the
issuance of debt securities to finance the purchase of the securitized assets from the
originator. The debt securities contain the feature of an interest-only balloon-payment
loan that requires no amortization of principal during the bond periods. The debt
securities will be fully redeemed at maturity. The bonds are usually fixed-rate bonds with
a term to maturity ranging from 7 to 10 years.
The ABS bond issuer relies only on the cash flows produced from the securitized incomegenerating property for the periodic coupon payments. The securitized property also
serves as collateral for the ABS bonds. The credit quality of the bonds depends to large
extent upon the fluctuation of the underlying property value. When default occurs, the
model assumes that the securitized property will be foreclosed and sold immediately. The
sale proceeds will then be used to make outstanding coupon payments and also redeem
the bonds at par value. With the non-recourse structure of the bonds, the ABS
bondholders will bear the risks associated with the shortfalls between property values and
ABS issuance bond values.
We employ the analytic framework of defaultable bonds to price credit risks of ABS
bonds. The model assumes that the ABS bondholders possess a risk-free debt security
and simultaneously write to the borrower (SPV) a put option on the underlying property
asset. The bondholders receive a coupon spread over and above the Treasury-bill rate as
the premium for the put option. If default occurs, the SPV could put the securitized
property asset to the bondholders at a strike price that is not more than the present value
of the remaining coupon obligations plus the face value of bonds at maturity.
For corporate bonds, one of the main problems faced in pricing credit risks using the
option pricing techniques is the difficulty in determining the value of miscellaneous
assets owned by firms that issues the bonds (Corcoran and Kao, 1997). Like non-recourse
loans, the ABS bondholders can only have recourse to the commercial property of the
SPV in the event of default. This simplifies the problem in the valuation of ABS credit
risk. Compared with other corporate bonds, the structure of ABS consisting of only one
6
real estate asset is more straightforward. Therefore, the ABS is a good case for the
application of option pricing approach to value credit risk.
In addition to the securitized claims on cash flows generated from the underlying assets,
ABS bonds are credit enhanced through both external and internal means like guarantee
of minimum rental cash flows by the head-lessee, a senior/subordinated structure, and
embedded sale-backed options (Sing, Ong and Sirmans, 2003). The credit enhancements
reduce uncertainty in the ABS transactions, and at the same time, increase the credit
rating of the bond tranches. The ABS bonds have also a higher credit rating than the
corporate rating of the originator because of the bankruptcy-remote feature built-in to the
ABS deals.
In the structural model, the default risk of ABS bonds can be priced based on the relative
value of SPV property to its issued bond/debt value. The model will not be flexible
enough to incorporate various credit enhancements for the bonds, such as corporate
guarantees included to assure ABS investors of timely payments of bond interests and
principals. The corporate guarantees will enhance the credit rating of ABS bonds, but
they are independent of whether the underlying property assets are able to produce
sufficient incomes to meet the bond payment obligations. The credit enhancements may
be an exogenous factor that will shift the optimal triggering boundary of the default
options. In other words, the property value may have to fall substantially below its
outstanding loan value before a default option will be exercised. This may imply that the
structural model may underestimate the credit risks of ABS bonds, when credit
enhancements of various forms are incorporated to the bonds.
In many credit risk pricing models, prices of underlying assets are assumed to evolve
following an exogenous stochastic diffusion process. The prices will only move
incrementally subject to predefined parametric constraints, when new information flows
in continuously. The price process precludes any sudden falls in prices, and therefore,
default never occurs unexpectedly. In the real world, however, shocks and bad news may
occur and cause abrupt downward adjustments of property price, which may in turn
7
trigger a sudden default by the bond originator. Therefore, when default event is
unpredictable, the reduced form approach may be more appropriate for valuing ABS
credit risk. In the model, the probability of default will be treated as an exogenous
variable linked to the rating-based information.
4.
Valuation Frameworks
Two credit risk pricing models are proposed to evaluate the default risks of the ABS
bonds in this paper: structural model and intensity model.
a)
Structural Model
In the structural model, credit risk of ABS bonds is driven by two state variables: the
underlying property value and the instantaneous risk-less interest rate. Credit
enhancements are not considered in this model. The default is triggered by the joint and
simultaneous occurrence of two events: when the underlying property value falls below
the market value of outstanding principal and interest payments of the bonds, and when
the net operating income from the property is less than the scheduled coupon payments at
any payment dates.
We extend the credit risk pricing framework of Shimko et al. (1993) and Kim et al.
(1993), which is used to price zero-coupon bonds, by incorporating discrete coupon
payments in the ABS bonds. Like the earlier models, we assume that the evolution of the
value of underlying property (V) follows a lognormal diffusion process, which is defined
in a specific form as follows,
dV = (a − b )Vdt + σ V VdZV ,
(1)
where a is the instantaneous expected rate of return of the underlying property, b is the
continuous payout rate for the property, σ V is the instantaneous standard deviation of
property return, and Z V is the standardized Wiener process. bV (t ) , in this model, defines
the net operating income from the securitized property.
We also assume that the instantaneous risk-less interest rate(r) evolves in a meanreverting diffusion process (see Cox, Ingersoll, and Ross, 1985).
8
dr = κ (µ − r )dt + σ r r dZ r
(2)
where κ is the speed at which the interest rate r reverts to the long-term mean rate, µ is
the long-term mean value of r, σ r is the interest rate volatility, and Z r is the
standardized Wiener process.
A risk-free portfolio consisting of a short position in the ABS bonds and a long position
in the underlying asset is constructed under the arbitrage-free conditions. The risk-free
portfolio yields an instantaneous risk-free rate of return on the portfolio over a short time
interval, dt, in a market where arbitrage is strictly eliminated. Using Itô’s Lemma on the
two stochastic variables, the ABS bond pricing equation can be defined by the following
partial differential equation (PDE),
1 2 2 ∂2S
∂2S 1 2 ∂2S
∂S
∂S
σVV
σ
σ
ρ
+
+ σ r r 2 + (r − b )V
+ (κ (µ − r ) − λr )
r
V
V r
2
2
∂V
∂r
∂V∂r 2
∂V
∂r
∂S
+
− rS = 0
∂t
(3)
where λ denotes the market price of interest rate risk, and ρ is the instantaneous
correlation coefficient between dZ V and dZ r .
On the assumption that the ABS bonds consist only of one single fixed-rate tranche with
coupons payments due semi-annually, Equation (3) is expanded to include the discrete
fixed-rate coupon payments as follows,
∂S
∂S
1 2 2 ∂2S
∂2S 1 2 ∂2S
+ (κ (µ − r ) − λr )
σVV
+ σ V σ r rVρ
+ σ r r 2 + (r − b )V
2
∂V
∂r
2
∂V∂r 2
∂r
∂V
∂S
+
− rS + ∑ C i δ (t − t i ) = 0
∂t
i
(4)
9
where C i is ith constant coupon payment during the bond periods4, δ (⋅) is the Dirac delta
function and t i is the time of the ith coupon payment (see, e.g., Cossin and Pirotte, 2001).
If ruthless default is not restricted, the bond originator can still choose not to fulfill the
redemption obligations at maturity (i.e., t=T), if and only if the following default
condition holds,
V (T ) < F + C
(5)
where F represents the outstanding bond values at maturity, C is the constant coupon
payment, and V(T) is the value of the underlying property at maturity.
Therefore, the value of ABS bonds, S(V, r, T) at maturity is a corner solution, which can
be defined as,
S(V,r,T) = Min {F + C , V (T )} .
(6)
At time t prior to bond maturity, the general solution for the ABS bond value with default
options can be derived by solving PDE (4) subject to two default conditions5: (a) the net
operating income, bV (t ) , is less than or equal to the scheduled coupon payment, C; and
(b) the value of the underlying property, V(t), falls to or below the value of ABS bonds,
S(V, r, t):
bV (t ) ≤ C
(7)
V (t ) ≤ S (V , r , t )
(8)
The two default conditions are jointly binding, which means that default will occur at a
coupon payment date only if both conditions are satisfied.6 Therefore, at time t prior to
bond maturity, [t < T], the equations can be written simply as follows,
4
5
6
As there are no earlier redemptions of the bonds in the ABS, the fixed-rate coupon payment, C i , is
assumed to be constant throughout the bond periods.
Leland (1994) suggests that default triggered by the condition that asset value falls to or below the debt
value will be irrelevant when the asset value becomes large. He includes an endogenous triggering
mechanism that is dependent on firm ability to raise capital to meet the debt obligations, which is
consistent with the condition in our equation (7), [ C ≤ bV (t ) ].
A similar default definition can be found in Westhoff et al. (2000), who developed a simulation-based
approach of estimating CMBS defaults.
10
V (t ) = Min [ S (V , r , t ), C / b]
(9)
Like in Titman and Torous (1989) and Childs et. al. (1996), the default may occur in the
absence of default cost, at a critical property value, which is way before the lower
triggering value is reached,
V * (r , t ) = S (V * , r , t )
(10)
where V * (r , t ) is determined endogenously.7
If either one of the conditions were not met, default will not occur. In other words, even if
the ABS originator was not able to meet the scheduled coupon payments with the net
operating income from the property, the default will still not be triggered as long as the
property value is still higher than the bond redemption value. Similarly, even if the
underlying property value falls below the value of ABS bonds, the originator will still
continue to keep the bond alive as long as the net operating income is higher than the
scheduled coupon payments.
After determining the value of defaultable ABS bonds, we could back-up the yield-tomaturity from the following pricing equation,
T
S t = ∑ C t e − yt + Fe − y (T −t )
(11)
t =1
where S t is the value of ABS bonds at time t, and F is the face value of ABS bond.8
The credit spread, which reflects the default premium over the remaining life of the
security, τ where [τ= T – t], can then be determined as the difference between the yieldto-maturity of ABS bond, y (τ ) , and the comparable yield on a Treasury bond with the
same maturity, r (τ ) ,
cs = y (τ ) − r (τ )
7
8
(12)
The critical V (r , t ) is determined endogenously using a spline methodology as in Childs et al.
(1996).
In order to calculate the yield-to-maturity from equation (10), we have developed a bisection algorithm
to approach the real solution of this equation.
*
11
b)
Intensity Model
The intensity-based model is an alternative approach to pricing the credit risk of ABS
bonds, where default is modeled as an exogenous Poisson process. The underlying
property value and the instantaneous risk-less interest rate are the two state variables in
the model, which are assumed to follow the same stochastic processes defined in the
previous structural model.
Following Wilmott’s (1998) approach in pricing the ABS bonds, S, a perfectly hedged
portfolio of a long position in underlying asset and a short position in risk-less zerocoupon bond with price Z (r , t ) is constructed, which is represented as follows,
Π = S (V , r , t ) − ∆Z (r , t ) .
(13)
where ∆ is the hedge ratio for the risk-less bonds.
Let the instantaneous default risk be p at time t, the default will be triggered at the first
jump of a Poisson process. For a simple case with only binary outcomes, the risky bonds
will either be or not be defaulted by the originator. The probability of default in a short
time interval from times t to t+dt can be represented as [pdt]. Conversely, [1-pdt]
indicates the probability of non-default of the ABS bonds. The value of the risk-less
hedge portfolio after the short time interval of dt, if default does not occur, can then be
derived as follows,
1

∂2S
∂2S 1 2 ∂2S
∂S
∂S
dΠ =  σ V2V 2
r
V
dV +
dr
+
+ σ r r 2 + C dt +
σ
σ
ρ
V r
2
∂V∂r 2
∂V
∂r
∂V
∂r
2

 ∂Z 1 2 ∂ 2 Z 
∂Z 
dr  ⋅
− ∆ 
+ σ r r 2 dt +
∂r 
∂r 
 ∂t 2
(14)
On the other hand, if default occurs with a probability of pdt, the change in value of the
portfolio can then be given as,
dΠ = − S + Q + O(dt1 2 )
(15)
12
(
where Q is the recovery amount of the ABS bond in default, and O dt1 / 2
)
is an
infinitesimal value relative to the loss of the ABS bond.
To solve the PDE (12), an optimal ∆ is selected such that the dr term in the equation can
be eliminated. By taking the expectation of the change in portfolio value, the basic
pricing equation for the ABS bonds with no interim coupon payments can be derived as,
∂2S 1 2 ∂2S
∂S
∂S
1 2 2 ∂2S
+
+ σ r r 2 + (r − b )V
+ (κ (µ − r ) − λr )
r
V
σ VV
σ
σ
ρ
V r
2
∂V∂r 2
∂V
∂r
2
∂V
∂r
∂S
+
− (r + p )S + pQ = 0
∂t
(16)
When the discrete coupon payments are taken into account, Equation (14) can be further
expanded as follows,
1 2 2 ∂2S
∂2S 1 2 ∂2S
∂S
∂S
σ VV
σ
σ
ρ
+
+ σ r r 2 + (r − b )V
+ (κ (µ − r ) − λr )
r
V
V r
2
2
∂V∂r 2
∂V
∂r
∂V
∂r
∂S
+
− (r + p )S + pQ + ∑ C i δ (t − t i ) = 0
∂t
i
(17)
which is subject to the following boundary condition,
S (V , r , T ) = F + C
(18)
For simplicity reasons, we assume that the instantaneous risk of default and the recovery
rate are constant. In other words, the instantaneous default risk and the recovery rate are
not correlated with the two specified stochastic variables.9 The credit spreads in a
continuous time intensity-based framework are also estimated by taking the difference
between the yield-to-maturity of ABS bond and the comparable yield of the Treasury
bond with the same maturity period.
9
The assumptions can be relaxed for more generalized cases. However, this study does not intend to
elaborate on the generalized cases, instead it focuses on the analysis of the effects on of these variables
on credit spreads.
13
5.
Estimation of ABS Credit Spread
In this section, we numerically analyze the credit spreads of ABS bonds using the two
proposed models. We consider a 10-year, 6% fixed rate coupon ABS bond backed by the
rental incomes from a securitized office property. The risk-less rate of return is
represented by the coupon rate of 3% for a Treasury bond proxy with a comparable
maturity term. In the ABS structure, the securitized property asset is transferred off-thebalance sheet of the original owner of the real estate asset. It insulates the bond investors,
on one hand, against any bankruptcy liability of the original owner. On the other hands,
bondholders will also have no recourse to the original firm’s asset in the case of default
on the bond obligations by the SPV. In other words, the ABS bondholders will only have
direct recourse on the income and sale proceeds from the securitized property, if it is
foreclosed.
The credit spreads of the ABS bonds can be estimated by solving equations (4) (structural
model) and (17) (intensity model). There are no analytical solutions to the two equations,
explicit finite-difference methods will be used to numerically compute the bond prices
and credit spreads from the two equations. For the numerical analyses, we make
necessary assumptions for the input parameters in the two stochastic processes, which
include: σ V , σ r , ρ , κ , µ , λ and b in equation (4), and σ V , σ r , ρ , κ , µ , λ , b, p and Q in
equation (17). We use the secondary data sources10: the Urban Redevelopment Authority
(URA)11 of Singapore data on commercial property prices, and the Monetary Authority
of Singapore (MAS) data on Treasury bonds over the past fifteen years to provide a close
approximation to the input parameters. In this paper, 5-year Treasury bond yield data
were used, because longer time series data were available compared to the 7-year and 10year Treasury bonds, which have only a relatively short history from the late 1990s.12
10
11
12
The secondary sources of information may include the Urban Redevelopment Authority (URA) of
Singapore published office property price and rental indexes and also the Treasury bond yields
published by the Monetary Authority of Singapore (MAS), the de-facto central bank of Singapore.
URA is the national planning authority of Singapore entrusted with the role to plan the long-term land
use and physical development of the country.
The 5-year Treasury bond yields offer a closer available proxy for the risk-less interest rate for the
ABS bond valuation, but we recognize that the Treasury bond yields with comparable maturity term of
10 years, if available, should be a better substitute (Titman and Torous, 1989).
14
6.
Results of Numerical Analyses
This section evaluates the sensitivity of the credit spread estimates to the changes of key
input parameters. The objective of these sensitivity analyses is to identify the important
factors and how these factors will have significant influences, in terms of both direction
and magnitude, on the credit spreads of the ABS bonds. The bond value is normalized to
one unit dollar, and the property value is set in a range from 0 to 2.5*F. The effects of the
changes in selected key variables, which include property value volatility, ( σ V ), the
correlation coefficient parameter, (ρ), and the recovery rate, (Q), on he ABS credit
spreads can then be illustrated.
For a base case scenario, we specify the parameter values for the relevant parameters
based on the historical data of Singapore office property market and the 5-year
government Treasury bond yields. The property payout rate, (b), is assumed to be 7%
based on the rental data, and the volatility of the office price is estimated at σ V =13%
based on the quarterly office rental return of the URA. The correlation coefficient of
[ ρ = 0.1 ] is assumed to reflect the historical correlations of the risk-less interest rate
changes and property returns over the last fifteen years, which was less than 10 percent.
The market price of interest rate risk is set to be [ λ = 0 ]. For the stochastic risk-less
interest rates, we use the quarterly yield data for the 5-year Treasury bonds to estimate
the reversion speed, [ κ =0.5], the long-term mean of risk-less interest rates, [ µ =0.037],
and the volatility of riskless interest rates, [ σ r =0.05]. For the intensity model, two more
parameters were assumed for the risk intensity, [p=0.01], and the recovery rate, Q=0.9].
a)
Effects of Property Price Volatility
By varying the property value volatility parameter from 0% to 45%, we evaluate how the
value surfaces of the ABS credit spreads will be affected in both the structural model
(Figure 1) and the intensity model (Figure 2). The maturity periods of the ABS bonds are
also added to show the time dimension of the volatility-credit spread relationships.
15
In the structural model, where no credit enhancement is included, the ABS credit spreads
increase with increases in volatility of the property value over time (Figure 1). However,
the rate of changes in the credit spread decrease as the volatility increases. In fact, the
positive relationships are no longer observed when the property value volatility exceeds
approximately 40%. When the property price volatility is above this level, the reverse
effects set in when the maturity of the ABS bonds is shortened. For example, at
σ V =45%, the credit spread premiums decrease from 4.62% for a 2-year ABS bonds to
4.41% and 3.56% for a 3-year and a 10-year ABS bonds respectively. We expect the
bond originator to keep the “default option” alive when the potential upside associated
with the high property price is valuable when the market is highly uncertain. The risk
premium for the ABS originator to default will also be higher when the bond maturity is
shortened.
[Insert Figure 1]
The positive credit spread-property price volatility relationships as shown in Figure 2 are
more discernible in the intensity model. However, in the relative scale, the credit spread
premiums of ABS bonds and also the rate of change of the premium over the volatility
changes estimated in the intensity model are much lower than those obtained in the
structural model. The effects are, however, independent of the maturity term of the ABS
bonds.
[Insert Figure 2]
The above results imply that ABS bonds without credit enhancement as represented by
the structural model are more sensitive to the shocks in the securitized property prices.
The rates of credit spread change are also dependent on the maturity term of ABS bonds,
if they are not provided with adequate credit enhancements. Clearly, ABS bonds with no
credit enhancements are riskier than those with credit enhancements. Therefore, credit
enhancements should be used as an effective mean to reduce default risks in the ABS,
especially in a high property price volatility environment.
16
b)
Effects of Correlation Coefficient between property values and risk-less rates
The effects of changing correlations between the risk-less interest rates and the
securitized ABS property return are analyzed by varying the coefficient, (ρ), from a
negative range of -0.4 to a positive range of +0.5. In the structural model (Figure 3), the
credit spread curves shifts in an upward direction along the correlation coefficient axis,
but the rate of change is marginal. For a case of 10-year ABS bond, the credit spread
premium increases from 0.0303 to 0.0322 when the correlation coefficient changes from
–0.4 to 0.4. The effects created by the correlations between the two stochastic processes
in the model were eliminated when credit enhancements were included in the intensity
model (Figure 4). The credit spread curves were the same over the entire range of
maturity periods, despite the changes in the coefficients of correlation.
[Insert Figures 3 and 4]
The difference in the estimates of the credit spread premium between Figure 3 and Figure
4 show the effects of having credit enhancement in ABS bonds on the credit spreads. This
suggests the importance of the credit enhancements in mitigating the default risks
associated with the correlations between property returns and risk-less interest rate
changes in ABS bonds.
c)
Intensity-based Factors Effects
In the intensity model, default is a Poisson process that is dependent on the instantaneous
risk of default, p, and the recovery rate in the event of default, Q. The probability of [1-
pdt] indirectly measures the level of credit enhancements within which default of ABS
will not occur. The credit enhancement effects will be evaluated by changing the
recovery rate in a range from 50% to 90% (Figure 5).
[Insert Figure 5]
The results show that the ABS credit spread is negatively related to the changes in the
recovery rates. The rate of decrease of the ABS credit spread as shown by the slope along
17
the recovery rate axis increases when the term to maturity increases. For a 2-year ABS
bonds, every 10% increase in the recovery rate, the credit spread premium decreases by
0.1%, whereas the rate of changes was approximately -0.14% for a 10-year fixed rate
coupon payment ABS bonds.
The results are not unexpected, which imply that ABS credit risk is lower when ABS
bondholders are assured that they can recover a substantial portion of the bond values
through foreclosure and disposal of the securitized property in the event of default, i.e. a
higher recovery rate. Compared to other paper-based non-recourse bonds, the probability
and the rate at which the bondholders can recover their investments from the securitized
assets are likely to be higher, since property price is less prone to inflationary risks. The
underlying property assets securitized indirectly credit enhance ABS bonds.
In summary, our results show that in the absence of credit enhancement, the ABS credit
spread is more sensitive to the positive shocks in the securitized property prices over
time. However, when credit enhancements are included, the effect of volatility on the
credit spread is significantly reduced. It is also shown that the credit spread is an
increasing function of the maturity term of ABS bonds. The effects of an increasing ABS
bond term are less critical when the price volatility level is high, [ σ V =45%], and when
credit enhancements are not available. Another significant and positive determinant of
ABS credit spread is the correlation between the risk-less interest rates and the property
return. The effect of the correlation can be eliminated by including appropriate credit
enhancements to the ABS structure. We also find that the credit spread is a decreasing
function of the recovery rates.
7.
Conclusion
This paper extended and applied two pricing models: structural model and intensity
model, to value credit spreads for ABS bonds. Numerical analyses were conducted with a
set of input assumptions that represent a base case scenario. Unlike the zero-coupon bond
models (Shimko et. al., 1993), the model is extended to allow for discrete coupon
payments during the life of the ABS bonds. However, the structural model does not
18
explicitly account for credit enhancements in the ABS bonds. In the intensity process, a
Poisson default process is included to represent the exogenous effects of credit
enhancements on the ABS credit risks. We could model different level of credit
enhancements by varying the intensity of default risks, p, and also the recovery rate, Q, in
the event of default.
We examine the sensitivities of the ABS credit spreads with respects to changes of key
parameters such as property price volatility, correlations between property price and riskless interest rate and also the intensity-based recovery factor. By varying the values of the
controlled variable within a plausible range, value surfaces of credit spreads estimated in
the two different models could be analyzed and compared. Credit spreads are highly
sensitive to the property price volatility, and the risk premiums are higher in the absolute
scale when credit enhancements are not included in the ABS structure. In the absence of
credit enhancement, credit spreads in a highly volatile environment, ( σ V =40%), decrease
with the length of the bond maturity term.
The credit spread analysis shows that the effects of an increase in the correlations
between property price return and risk-less interest rate on the ABS credit spreads were
positive, but at a marginal rate of change. These positive effects were eliminated in the
intensity model when credit enhancements are included. Based on the above sensitivity
analyses, credit enhancements are important features in ABS that will improve the credit
quality and mitigate possible losses of ABS investors in the event of default. The
effectiveness of the credit enhancements is, however, dependent on the loss recovery rate
when default occurs. ABS bonds backed by physical property are likely to have lower
credit risk than non-collateralized ABS bonds, because bondholders is assured that they
can recover a substantial portion of the bond values through foreclosure and disposal of
the securitized property in the event of default, i.e. a higher recovery rate.
19
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22
Figure 1 Sensitivity Measures of Credit Spreads vs. Varying Property Value
Volatility (Structural Approach)
23
Figure 2 Sensitivity Measures of Credit Spreads vs. Varying Property Value
Volatility (Intensity Approach)
24
Figure 3 Sensitivity Measures of Credit Spreads vs. Varying Correlation
(Structural Approach)
25
Figure 4 Sensitivity Measures of credit Spreads vs. Varying Correlation
(Intensity Approach)
26
Figure 5 Sensitivity Measures of Credit Spreads vs. Varying Recovery Rate
(Intensity Approach)
27