Chapter 4

Chapter 4 Analysis of Credit Risks in ABS Transactions 81

Chapter Four

ANALYSIS OF CREDIT RISKS IN ABS

TRANSACTIONS1

4.1 Introduction

The previous chapters have mentioned that ABS in Singapore is mainly referred to a

contractual arrangement whereby debt instruments backed by cash flows generated from

real estate assets are securitized into tradable interests and offered for investment purposes

in the capital market. Asset-backed securities provide an alternative funding source for

commercial property owners in Singapore. However, ABS is a relatively new financial

innovation in Singapore. The public ABS debt issues in 1999 have not yet matured, and

credit risks associated with prepayments and defaults are still uncertain at this stage.

Undertaking an empirical analysis of the loss experience is impossible in the absence of

empirical data. Traditional valuation models, on the other hand, are still far from being

fully developed to theoretically evaluate these embedded risks. The credit risks in the

Singapore’s ABS are further complicated with unique leaseback and buyback options2

built into the contracts (Sing, Ong and Sirmans, 2003). The two features bring more

uncertainties into the payment patterns and structure, which consequentially complicate

the credit risks evaluation for the Singapore’s ABS deals.

1 A revised version of this chapter has been published by an international journal: “Analysis of Credit

Risks in Asset-Backed Securitization Transactions in Singapore,” with Sing, Tien Foo, Ong, Seow Eng, and Sirmans, C. F., Journal of Real Estate Finance and Economics, 2004, 28(2/3), pp.235-253.

2 The lease-back options embedded in the securitization agreement entitles the ABS originator to lease back the property wholly or partially from the SPV for a specified period; and the buy-back option is analogous to a call option, which confers the ABS originator a right to buy-back the property at the original price and reap capital appreciations on the securitized property.

Chapter 4 Analysis of Credit Risks in Asset-Backed Securitization Transactions 82

The development of the derivative pricing theory has offered new insights to default risk

in swaps. Swap contracts, which facilitate exchanges of a series of cash payments of

different characteristics between counter-parties, are financial instruments that are highly

sensitive and susceptible to credit risks: default and interest rate risks. Theoretical

modeling and research on default and interest rate risks have been growing significantly in

financial literature (see, for example, Black and Cox, 1976; Johnson and Stulz, 1987;

Cooper and Mello, 1991; Hull and White, 1993, Kim, Ramaswamy, and Sundaresan,

1993; Abken, 1993; Duffie and Huang, 1996; Duffie and Singleton 1999, Hübner, 2001).

In real estate literature, Baum, Beardsley and Ward (1999) apply the swap model to value

typical leases embedded with option-like features in the UK. In the proposed swap model,

they demonstrate how rental cash flows can be partitioned and swapped for other fixed or

floating payments.

The ABS deals in Singapore generate cash flow patterns that are comparable to a swap

contract. Firstly, upon exercising the embedded leaseback options, the originator pays a

stream of floating cash flows to the SPV in return for an exclusive right of use of the

property for a specific lease period. The SPV then converts these floating cash flows to a

fixed cash flow stream payable to the bondholders as their coupon yields. In the swap

analogies, the bondholders in the ABS purchase a cash flow floor (fixed rate) from the

SPV and the originator (lessee) writes a cash flow cap (floating rate) to the SPV. The

credit risks of ABS could then be valued in a swap framework taking into account

uncertainties associated with the fixed coupon rate, floating rental rate and even notional

principal (ABS prices or transacted property price). This chapter applies the default-risky


swap framework proposed by Duffie and Huang (1996), Duffie and Singleton (1999) and

Hübner (2001) to evaluate credit risks associated with the ABS deals.

This chapter is organized into five sections. Section 4.1 gives the background and

objectives of the study. Section 4.2 presents the structure of the ABS and also sets up the

basic swap framework for the ABS valuation. Section 4.3 derives the proposed default-

risky swap valuation models, and Section 4.4 applies the proposed default-risky swap

models to estimate the risk premiums in a sample ABS case using numerical

methodology. Section 4.5 concludes the findings.

4.2 Valuing ABS in Swap Framework

4.2.1 Relevant Structure Features

In a typical ABS, an owner or developer of a high quality real estate originates debt

securities backed by a steady stream of cash flows generated via a special purpose vehicle

(SPV). The SPV creates a “bankruptcy remote” structure that facilitates an off-balance-

sheet transfer of the real estate being securitized from the originator. This arrangement

distinguishes it from the traditional collateralized loans and mortgage pass-through

securities, where the real estate is retained on the balance sheet of the originator (Sing,

Ong and Sirmans, 2003). SPV will raise funds by issuing debt securities backed by the

real estate to fund the purchase of the real estate. The (floating) cash flows received from

the real estate, which normally fluctuate with the changes in occupancy rates and leased

rents, will be passed-through via the SPV to the bond investors in the form of fixed

coupon payments. Figure 4.1 gives a diagrammatic representation of a typical ABS deal in


Singapore. Two “exotic” options are incorporated in the ABS agreements. The leaseback

option confers a privilege to the owner (originator) to continue to use the real estate as a

main lessee subject to agreed market rents. A buy-back option, which is analogous to a

“call-back” right on the bond issues, is also embedded in the ABS contract to allow the

owner to repossess the real estate at the original market price plus a pre-specified premium

upon exercising of the option.

Figure 4.1: Structure of an Asset-Backed Securitization Deal

InvestorsInvestors

(Purchasing (Purchasing ABS bonds ABS bonds

for fixed for fixed returns)returns)

Originator Originator (Company (Company securitizingsecuritizing

its real its real estate)estate)

Special Purchase

Vehicle (SPV)

Investments in secondary market

instrument

Rental Cash Flow received from the securitized real

estate leases

Sale Proceeds from the sale of

securitized real estate

Bond/ Dividend Yield

Real Estate Market

Secondary Market

Lease-back option

Buy-back option

Exchange of cash flows between originator and investors via SPVTransfer of embedded options

Boundaries between primary and secondary markets

Notes:

Source: Sing & Ong, 2001

Independent credit rating agencies are generally involved in the securitization process to

assess credit risks of the ABS bond issues. This credit rating process has not been

enforced in the earlier ABS issues in Singapore. Credit enhancement is given in the form

of guaranteed cash flow payments to meet the coupon payment obligations on the bonds.


The established credit standings of the real estate owner (originator), which are publicly

listed companies, also provide limited assurance against default risks to investors of the

ABS bonds. These credit enhancers reduce credit risks of the ABS bonds, but they are still

short of being fully risk-less bonds. If the cash flows generated from leasing the real estate

fall below the floor (fixed-rate coupon) written on the ABS bonds, the bondholders will be

exposed to unexpected default risks. For the fixed coupon rate ABS bonds, default risks in

the ABS can be quantified as a function of two stochastic state variables: leasing (floating)

rate and default-free interest rate.

For evaluating the credit risks of the ABS, this study simplifies the cash flows between the

originator (building owner) and the bondholders by making the assumption that the

originator will exercise the buy-back option and repurchase the real estate at original

market price at the end of the bond maturity.3 This assumption thus implies that the

bondholders’ initial principal will be redeemed at par value at maturity. ABS transaction is

thus reduced to a simple swap of floating cash flow generated from leasing the real estate

for a fixed rate cash flow passed-through to bondholders. The cash flow swaps are

facilitated by the SPV, which act as an intermediary. With the swap characteristics, the

default and cash flow (interest) rate risks in ABS can be readily evaluated and examined

as swap contracts or swaptions.

3 In the ABS cases, the originator (real estate owner) will have to pay the SPV the original market price

plus a percentage of capital gain at the date the buy-back option is exercised. This capital gains portion to be distributed back to the bondholders is omitted in this study, and its omission will not severely affect the results of the analysis.


4.2.2 Swaps or Swaptions

A financial swap is a contract that facilitates the exchange of cash payments consisting of

usually one fixed rate payment and one floating rate payment between two counterparties

for a notional sum of value (Figure 4.2). An option of swap, which is known as swaption,

gives the holder a right to swap a floating cash flow for a fixed cash flow or vice versa at a

specified rate at a particular date in the future. The plain vanilla interest rate swap contract

is composed of a floor written by the fixed ratepayer and a cap written by the floating

ratepayer. In an equity swap, equity investors who contemplate a decline in the equity

market may enter into a swap arrangement whereby he agrees to pay equity returns

(dividends and capital appreciation) for a London Interbank Offer Rate (LIBOR) or a

fixed rate return.

Figure 4.2: Structure of Swaps Framework for Asset-Backed Securitization Swap

Company A Company BFixed Rate Payment

Floating-Rate (LIBOR) Payment

a) Interest Rate Swap Contract

b) Cash Flows Swap in ABS Deal

1

2

Off-balance-sheet transfer of asset

Exercising lease-back option

Floating-rate Rental Payments

Special Purpose Vehicle (SPV)

Originator/ Head lessee

Bond Investors

Sub-lessees

Sale Price for Securitized Real

Estate

Notional Principal of Bonds

Fixed-rate coupon

payments

Rental Revenue

from Sub-leases

1

2


The ABS in Singapore consists basically of two cash flow streams, which can be

decomposed into a floating rate cash flow represented by the rental revenue and a fixed

rate cash flow represented by the coupon payment. The swap of the two cash flows is

intermediated by the SPV as shown in Figure 4.2. Via this swapping process, the real

estate owner (originator) could securitize the illiquid low yield real estate, which allows

the owner to pay floating rental cash flow in exchange for a fixed-rate bond principal from

the bondholders who prefer long-term steady periodic coupon payments. Studies on

pricing of interest rate swaps and associated credit risks have been abundant (Smith,

Smithson and Wakeman, 1986; Cooper and Mello, 1991; Sundaresan, 1991; Abken, 1993;

Sorensen and Bollier, 1994; and Duffie and Huang, 1996). The techniques developed

provide important insights and lessons for this study. Following the approaches developed

by Sundaresan (1991), Duffie and Huang (1996) and Duffie and Singleton (1999) and

Hübner (2001), this study attempts to conceptualize a robust framework that can be

applied to analyze credit risks of ABS in Singapore.

4.3 Basic Valuation Framework for Swaps

A default-free interest rate swap can be expressed as a portfolio of bonds, which

comprises a long position in a fixed-rate (or floating-rate) bond and a short position in a

floating-rate (or fixed-rate) bond. It can also be evaluated as a series of forward rate

agreements (FRAs)4 with maturities corresponding to the settlement date specified in the

swap contract (Smith, Smithson and Wakeman, 1988). For FRAs with a flat term structure

4 Forward rate agreement (FRA) is a single period bilateral agreement where one party agrees to pay or

receive the difference between an agreed fixed rate (the FRA rate) and LIBOR in the future calculated on a fixed interest period.


of interest rates, the fixed interest rate of the swap can be determined such that the initial

value of the swap is zero.

Theoretically, the equilibrium swap rate is determined by equating the present values of

cash flows between the fixed-rate leg and the floating-rate leg of a swap. Sundaresan

(1991) shows that equilibrium swap rate can also be determined as a convex combination

of forward interest rates. Let the fixed swap rate be represented by r and the forward rate

by r̂ . In a two-period fixed-for-floating default-free swap case, the swap may be valued

as,

( ) ( ) ( ) ( ) 21 ˆ2ˆ121 rbrbrbrb +=+ (4.1)

where ( )xb is denoted as a discounted bond price (notional principal) in future periods x =

[1, 2]. Dividing the two sides of equation (1) by [ ( ) ( )21 bb + ], the equilibrium fixed swap

rate r can be estimated as follows, which is a convex combination of the forward rates

(Sundaresan, 1991),

( )( ) ( )

( )( ) ( ) 21 ˆ

212ˆ

211 r

bbbr

bbbr

++

+= . (4.2)


In the absence of default risk, the swap cash flow in equation (4.1) can be further

generalized into a multi-period (N-period) swap case as,

( ) ( ) i

N

i

N

i

ribrib ˆ11∑∑==

= (4.3)

The equilibrium swap (fixed) rate in equation (4.2) can be represented by a weighted

average of the forward rates ( ir̂ ),

( )

( )∑

∑

=

== N

i

N

ii

ib

ribr

1

1

ˆ (4.4)

In the ABS context, the SPV and the originator (also the head lessee of the securitized real

estate) are equivalent to the fixed-rate and floating-rate payers respectively in a swap

contract. Assuming that the originator exercises the lease-back option, he obtains the

exclusive right of use of the real estate for a period not exceeding the bond maturity and

pays market rents to the SPV, which is now the legal owner of the real estate. The SPV

converts and passes-through the rental cash flows to the bondholders as fixed rate coupon

payments. Technically, the SPV swaps the floating cash flows from the originator (head

lessee) with the fixed rate cash outflows to the bondholders. In equilibrium, the fixed rate

coupon payment for the bondholders equates the present values of the cash flows from

leasing the securitized property assets, so that the swap value is zero in the absence of


default risk. The equilibrium default-free swap value can be represented by equation (4.5)

as,

( ) N

N

ii

N

i

VNbNRIibVNbFRPib +=+ ∑∑ )()()( 0 (4.5)

where FRP is the fixed-rate payment, iNRI is the net rental income at future period i, 0V is

the principal of bond issued by the SPV, and NV is the price of securitized property assets

at maturity. Dividing both sides of equation (4.5) by ( 0V ), the equation could be rewritten

as,

( ) ( ) ( ) ( )δNbRibNbribN

ii

N

i

+=+ ∑∑ (4.6)

Compared with equation (4.4), r represents the equilibrium fixed coupon rate for bonds,

iR denotes the floating rental return and δ reflects the proportion of real estate price over

the bond principal, or the equivalent original real estate price (assuming that the bonds are

issued at par value), at the maturity period.

4.4 Credit Risks in ABS – A Swap Valuation Approach

Swap is invariably an over-the-counter derivative instrument. Default risks are highly

sensitive to the swap rates agreed by the counterparties in the contracts. These are indeed

one of the main concerns of the counterparties, the financial intermediaries that broker the


swap deals, as well as the financial regulators that enforce a transparent and fair dealing in

the swap market. On the one hand, the counterparties may mitigate the default of swap by

requiring various credit enhancers to be incorporated in the swap, or dealing only with

counterparty of high credit standing. These mitigating measures or criteria provide

protection against possible losses, but they do not eliminate fully the default risks in

swaps. On the other hand, the strict credit enhancement requirement imposed on the

contract increases transaction costs in the warehousing process because of the lower

matching rate for cash flows to be swapped. It is thus important to be able to explicitly

value the default-risky component residing in swap contracts, so that adjustment to the

swap rates or other credit enhancers could be provided to compensate for or prevent the

counterparties from possible defaults.

The same logic applies to the ABS deals, whereby counterparties should not take

advantage of the privilege information to structure a deal that are one-sided (asymmetric),

i.e. default-risky to only a party. Valuing default risks in ABS deals becomes highly

important since most of the ABS bond issues thus far in Singapore were not assessed and

rated by credit agencies. Many theoretical models have been developed in derivative and

swap literature to evaluate swap cash flows in a default-risky framework.

The existing approaches to valuing default risk associated with swap can be divided into

two classes. The first class of default-risky swap models (Abken, 1993; and Cooper and

Mello, 1991) decomposes the cap and floor in an interest rate swap and discretely

delineates the default risks associated with the counter-parties in the swap contracts. The

default risks could then be valued independently from the perspective of one party while


keeping the counter-party default-free. These one-sided default risky models are robust

when the default occurs predictably, but they are ineffective in pricing default risks that

are associated with “sudden events” (Zhou, 1997). In practice, the defaults between the

counter-parties are often not symmetric, and the bilateral default risks may co-exist in the

swap contracts. When default risks are asymmetric, credit rating information is crucial in

determining a reasonable credit spread that is risk-neutral for the two counter-parties in the

swap (Jarrow and Turnbull, 1995; Jarrow, Lando and Turnbull, 1997; Duffie and Huang,

1996; Duffie and Singleton, 1999; and Hübner, 2001). The models of Duffie and Huang

(1996), Duffie and Singleton (1999) and Hübner (2001) that incorporate credit ratings and

financial market information of the default-able debt instruments fall into the second class

of the bilateral default-risky swap models.

In Duffie and Huang (1996) and Duffie and Singleton (1999) models, default is assumed

to follow an exogenous process defined by a hazard rate function, and the loss recovery in

the event of default constitutes only a fraction of the market value of the bonds. The zero-

coupon default-able bond price model of Duffie and Singleton (1999) is represented as

follows

( ) ( )

−= ∫ XdssRexpETV

TQ

000 (4.7)


where Q denotes an equivalent martingale measure,5 QE0 represents the risk-neutral

expectation under Q and conditional at time 0, ( )tR represents a default-adjusted short

rate, which is the sum of a short-term riskless interest rate and a default risk premium,

and X is the promised payment at maturity T. The equivalent martingale measure, Q, in

equation (4.7) implies that there are no arbitrage opportunities in capital markets (Harrison

and Kreps, 1979; and Duffie and Huang, 1996). In this risk-neutral framework, the

discounting of the defaultable claim using a default-adjusted discount rate can be treated

as if the expected payoff is discounted at a riskfree rate.

Hübner’s (2001) extends the Duffie and Singleton (1999) framework by separating credit

assessment and swap valuation into a two-stage process to derive at an analytical pricing

model for asymmetric default-able swaps. The swap pricing equation is derived in his

model as follows:

( ) ( ) ( )

∫= ∫−

tj

T

t

duuR

Qj sdDeEtVs

t j ξ (4.8)

where Dj is the non-negative process of all promised defaultable payments to one of the

counter-swap parties j, ( )tR j is the default-adjusted discounting rate, and (ξt) represents

information available up to time t. The above Hübner’s (2001) formula is applicable for

bilateral contracts that adhere to the “full two-way payment rule” stipulated under the

International Swap Dealers Association (ISDA) agreement. Under the rule, the swap

counter-party can only default on his/her obligation, and upon default, he/she will receive

5 The completeness of the financial markets implies that we could find a unique probability measure Q,

equivalent to the historical probability measure P, such that under this probability measure the discounted price of any financial asset becomes a martingale, which is a zero-drift stochastic process. The probability measure Q is known as the equivalent martingale measure.


a full closed-out payment if the pre-default value of the swap is positive. The probability

of default determined by a stochastic variable would have implications for the default

spread. Whereas, under “limited two-way payment rule,” the credit spread is dependent on

the parties’ default risks, because the defaulting party will not be entitled to claim

payments of his/her in-the-money swap. Duffie and Huang (1996) and Duffie and

Singleton (1999) model the “limited two-way payment rule” by integrating the default risk

endogenously into the swap value.

The bilateral default risks under the “full two-way payment rule” exist in the ABS cases,

which imply that each party in the ABS deals is exposed to the credit risk of the opposite

party. In ABS structure represented in Figure 4.1 earlier, there are although three parties

involved in the financial structure: the lessee (floating rate payer), the bondholder (the

fixed rate receiver) and the SPV, the role of the SPV is limited to a passive intermediary

that facilitates the conversion and transfer of the cash flow between the fixed rate and

floating rate payers. The SPV is a bankruptcy-remote entity, which does not bear any

credit risks with respect to the other parties’ default decision. Although, the SPV does not

stand in between the two parties as far as credit risks are concerned, default of the fixed-

rate payers (the SPV), which will disrupt the stream of cash flows, can still be triggered by

the action of the floating-rate payers (the lessee) under this structure. However, the default

risk faced by the fixed rate receiver (bondholder) is not critical because there are sufficient

protection in placed in the ABS contract. The fixed rate receiver possesses a put option,

which gives him a right to recover his cash flows by exercising the option to redeem the


outstanding bonds.6 In a restrictive sense, the ABS arrangement thus fits the “full two-way

payment rule,” although the default probability mainly lies with the floating ratepayer.

Hübner’s (2001) bilateral default-risky swap model can therefore still be adopted in this

study to evaluate the default risks and estimate the equilibrium fixed coupon rate at which

default risks in the ABS deals can be offset.7

In the proposed default-risky swap model, two stochastic state variables are defined. The

adjusted rental return rate (R) is the first state variable, which is assumed to follow a

specific stochastic process with a mean-reverting tendency as below,

( ) 1RdzdtRdR Rσµα +−= (4.9)

where α is the speed of rental adjustment,µ is the long-term average rental rate, 2Rσ is

the instantaneous variance coefficient for rental changes, and 1dz is the increment of a

standard Wiener process. [ ( )R−µα ] is the drift term, which represents a mean-reverting

force that pulls the rental return towards its long-term value. Compared with the standard

mean reverting process of Cox, Ingersoll and Ross (CIR) (1985), the lognormal diffusion

process has been replaced with a normalized diffusion process by using a “R”, instead of

the usual “ R ” term, in the second right hand side variables of equation (4.9). This

6 There is also guarantee on the part of the ABS originator to oblige its fixed rate coupon payment to the

borrower in the event of shortfalls in the collection of rental from the floating rate payer (the lessee). 7 The cash flows will be deemed to follow the “limited two-way payment rule,” only in the circumstances

where the SPV is not a passive and risk-neutral entity. As pointed out by one of the anonymous referees, Hübner’s (2001) model will then be limited in its application under such condition where the risk exposure is unevenly distributed among the three parties. In that case, Duffie and Singleton (1999) approach, which matches the net exposure of the credit risk impact between parties, will offer a more appropriate assessment of default risk under this rule.


dynamic R assumption is one class of linear stochastic differential equations (Arnold,

1974), which has been used by Brennan and Schwartz (1980) in their equilibrium term

structure model of interest rate. This mean reverting process is flexible enough to capture

the negative rental rates and better reflects the historical office rental returns in Singapore,

which tend to drift and revert back to the long-term average level (Figure 4.3). Chan et al.

(1992) found empirically that the stochastic process in Brennan and Schwartz model better

fits the short-term interest rate compared with the CIR stochastic process.

Figure 4.3: Mean Reverting Trends in Office Rental Returns (1989Q2-1999Q2)

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

1989

Q2

1990

Q2

1991

Q2

1992

Q2

1993

Q2

1994

Q2

1995

Q2

1996

Q2

1997

Q2

1998

Q2

1999

2Q

Sources: Urban Redevelopment Authority (URA) / Inland Revenue Authority of Singapore (IRAS)

The second state variable is the risk-less discount rate (r), which is assumed to follow the

standard CIR stochastic process represented as follows,


( ) 3dzrdtrdr rσθκ +−= (4.10)

where θ ,κ and rσ are the positive constants, and 3dz is the increment of a standard

Wiener process. The CIR model is shown by Gibbons and Ramaswamy (1993) to have

satisfactorily described the term structures of short-term T-bills under the frictionless

capital market condition, where assumptions like no taxes, no transaction costs, no

bankruptcy costs, no arbitrage opportunities, and trading takes place continuously, hold.

In ABS transactions, the transfer of ABS cash flows from the originator (lessee) to the

bondholders can be replicated by a cash-flow portfolio consisting of a short position on a

fixed rate bond and a long position on a floating rate bond. Let VNRI(t) and VFRP(t) denote

the present values of both the floating and fixed rate payments to the SPV and

bondholders respectively. The default-risky component of the basic “swap” pricing

formula for ABS can be represented as

( ) ( ) ( )tVtVtV FRPNRI −= . (4.11)

When ( ) 0<tV , the bondholders are vulnerable to the SPV’s default risks. When the value

is positive, that is ( ) 0≥tV , the ABS transaction will be favorable to the bondholders and

the SPV. At the bond maturity, this study assumes that the originator will undertake to

redeem the outstanding bond issues by exercising the buy-back option to repurchase the

securitized property at original price. The proceeds in the repurchasing of the securitized

property will then be transferred through the SPV to bondholders.


Using the classical martingale approach, we expand Equation (4.11) to derive at the

following swap pricing equation,

( ) ( ) ( )

−−

−= ∑ ∫∑ ∫

==

N

ii

i ciQi

N

i

i

iiQ dssrexpFRPEdssRexpNRIEtV1

01

0ξξ (4.12)

where Q denotes an equivalent martingale measure, cir represents the default-adjusted

interest rate of the replacement bond composed of a riskless interest rate ( ir ) and a

constant credit spread (h), i.e. [ hrr ic

i += ], iR represents the adjusted rental return rate,

and iξ reflects the information revealed up to time i. A constant credit risk spread (h)

variable, which is defined as the difference between the fixed coupon yield and the risk-

less interest rate, is included to compensate the fixed-rate receiver (bondholders) against

default risks. In Hübner (2001) model, the credit risk spread that accounts for the

probability and timing of default and the fraction of asset recovery on default is

determined by stochastic state variables.

Equation (4.12) implies that the swap value for the SPV is positively related with the net

rental (floating rate) cash flows, but negatively related with the fixed-rate coupon

payments. One variation found in the above model compared to the interest rate swap

models of Duffie and Singleton (1996) and Hübner’s (2001) lies on the exchange of the

principal payments between the parties of the ABS deal at two points in time of the ABS

transaction. At the beginning of the ABS contract, the originator (who is also the lessee)

receives a full payment for the sale of the property to the SPV, and the cash proceeds are

obtained from the issuance bond principals. At the maturity of the bond, the originator


repurchase the property at a strike price plus a fraction of capital appreciation, of which

the cash flows will be used to redeem the outstanding bonds through the SPV.

Based on the above cash flow assumptions, the equilibrium default-free cash flow swap

value in Equation (4.5) that equates the fixed-rate leg and floating-rate leg cash flows can

then be expanded as follows,

( ) ( ) ( ) ( ) Nl

N

iilx

N

ix VNbNRIibVNbFRPib ,0,0,0,0

10

1+=+ ∑∑

==

(4.13)

where ( )ibx ,0 and ( )ibl ,0 represents the discounted bond prices for the fixed-rate leg and

the floating-rate leg respectively. Similarly, the equilibrium coupon (fixed-payment) rate

can be determined with the following revised Equation (4.12),

( ) ( )

−=

− ∑ ∫∑ ∫

==i

N

i

i

iiQi

N

i

i ciQ dssRNRIEdssrFRPE ξξ

10

10

expexp . (4.14)

The equilibrium coupon rate can be solved numerically using the Dekker and Brent

(Brent, 1993) algorithm as suggested in Abken (1993).

4.5 Numerical Analysis of Default Risks in a Typical ABS Case

The proposed default-risky swap model given in Equation (4.11) does not contain

standard analytical solutions. The swap value and the equilibrium swap rate that

compensates for the default-risky floating rate components could be jointly determined


using the Monte-Carlo simulation technique.8 For illustrative purposes, the proposed

default-risk swap model is applied to an actual ABS case originated by First Capital

Corporation (FCC), the owner of the Century Square shopping mall, which was valued at

S$200 million in the open market.

Table 4.1: Input Parameters for Monte-Carlo Numerical Analysis

Input Parameters Base Value A) Historically Estimated Parameters: Sale price for the securitized real estate V0 = S$200,000,000 Initial rental rate Ro = 7% Average long-term rental rate µ = -1.31% Annualized Rental volatility Rσ =14.02% Fixed-rate coupon yield cr =5% Initial (stochastic) default-free interest rate ro = 3.7% Average 5-year default-free Interest Rate θ = 3.78% Default-free interest rate volatility rσ =0.83% Correlation coefficient between stochastic interest rate and rental rate

ρ = -15.9%

Credit Spread h=5.3% B) Calibrated Parameters: Speed of mean reverting of rental return α = 8% Speed of adjustment of risk-less interest rate κ = 40%

To implement the Monte-Carlo simulation, estimates of the relevant parameters for the

two stochastic processes are necessary. Based on the quarterly rental index of the Urban

Redevelopment Authority (URA) and the quarterly yield rates of the 5-year bond of the

Monetary Authority of Singapore (MAS) from 1990 to 2002, the parameters like rental

volatility ( Rσ ), default-free interest rate volatility ( rσ ), average rental rate (µ), risk-free

rate (θ), and correlations between the rental and risk-free rate (ρ) are ex-post estimated. In

8 The process of Monte-Carlo Simulation analysis is described in Appendix 1.


the absence of the empirical data for the two mean reverting adjustment parameters (α and

κ) and the credit spread (h) parameter, Monte-Carlo simulation methodology is used to

calibrate these parameters by assuming that the observed values of the ABS transaction

will be matched in an equilibrium condition. The Monte-Carlo simulation algorithm is

carried in stages by fixing two parameters at any one stage to obtain the remaining

unknown variable. The process is repeated progressively by varying different set of

unknown and fixed parameter values.9 This set of input parameters as summarized in

Table 4.1 forms the base case scenario for the bilateral default-risky swap model (equation

(4.12)) in the numerical analyses.

Based on the above input parameters, the Monte-Carlo simulations were carried out and

the results are summarized in Table 4.2. The default-risky component (default risk

premium) of the swap value in the table is defined as the difference between the present

values of floating-rate leg cash flows and those of the fixed-rate leg cash flows discounted

by the default-adjusted short rates10. When the value of the default-risky component of

swaps is positive, the cumulative discounted present value of the floating-rate cash flows

is greater than that of the fixed-rate cash flows and the rental incomes are sufficient to

cover the bondholders’ coupon payments. The default-risk component is positive when the

market is favorable, and the ABS transaction is more valuable to the SPV. The larger the

9 The simulation exercise is undertaken on the assumption that the market is at equilibrium, and the

calibrated values for the input parameters may not be fully used to mark-the-market price of the ABS securities in the subject case. However, the results do reflect the sensitivities of the change of the securities price to changes in various parameter values. This was the concern pointed out by one of the anonymous referees.

10 The defaulted-adjusted short rates are the sum of the risk-free rates and default risk premiums, which are consistent with the risk-neutral assumptions. Discounting the cash flows by the default-adjusted short rate will account for the probability and timing of default as well as the loss recovery in default (Duffie and Singleton, 1999).


positive value of the default-risky swap component, the larger is the protection for the

fixed-rate payers against default, which means a lower default risk. When the default-risky

swap component value is negative, there is a high likelihood that rental incomes are

insufficient to meet the coupon obligations, and thus expose the bondholders to high

default risks. For a deterministic scenario, where the volatilities for the rental and risk-less

interest rates are zero, the default risk premium (buffer) in the swap contract was

estimated at S$4.25 million or equivalent to 2.13% of the initial securitized real estate

value.

The sensitivity of the swap value to change in the volatilities can be numerically analyzed

by simulating the rental and risk-less rate volatilities over a discrete range of 5% to 50%.

The results in Table 4.2 show that the default-risky components of swap are more

sensitive to variation in the rental volatility than the default-free interest rate volatility.

The default-risk values vary from S$4.4 million to -S$7.5million when the rental volatility

increases from 10% to 50%, given that the default-free interest rate volatility is fixed at

30%. Compared with the sensitive effect of S$11.9 million in relation to the changes in

rental volatility, the default-risky swap value changes only by S$2.22 million (from

S$0.19 million to S$2.03 million) when the risk-less rate volatility increases from 10% to

50% holding the rental volatility unchanged at 30%.


Table 4.2: Results of Monte-Carlo Simulations for Discounted Swap Values

Reduced-form Swap Model

Rental rate volatility

Default-free interest rate volatility

Swap Value

(S$million) (%)@ a) Deterministic Scenario

0% 0% 4.25 2.13% b) Stochastic Scenario

5% 3.75 1.88% 10% 3.65 1.83% 20% 3.78 1.89% 30% 4.40 2.2% 40% 5.09 2.55%

10%

50% 5.80 2.9% 5% 2.35 1.18% 10% 2.25 1.13% 20% 2.44 1.22% 30% 3.04 1.52% 40% 3.71 1.86%

20%

50% 4.28 2.14% 5% -0.26 -0.13% 10% -0.19 -0.1% 20% -0.21 -0.11% 30% 0.42 0.21% 40% 1.18 0.59%

30%

50% 2.03 1.02% 5% -3.65 -1.83% 10% -3.94 -1.97% 20% -3.60 -1.8% 30% -2.86 -1.43% 40% -2.29 -1.15%

40%

50% -1.66 -0.83% 5% -8.52 -4.26% 10% -8.45 -4.23% 20% -8.28 -4.14% 30% -7.50 -3.75% 40% -6.96 -3.48%

50%

50% -6.17 -3.09% @ Estimated swap value expressed as a percentage of the notional bond issue value (S$200 million).


At the historical annualized rental volatility of 14.02%, the value default-risky swap

component will always remain at the positive region, which implies that the default risks

faced by the fixed-rate receivers are insulated. The default-risky swap value will only dip

into a negative region when the rental volatility increases above 30%, while the default-

free interest rate volatility does not exceed 20%. In this scenario, default risks will be

significant, and credit enhancers should be added to protect the fixed-rate receivers

(bondholders).

Figure 4.4 shows the value surface of the default-risky component of the swaps in relation

to the changes in the rental and risk-less rate volatilities for a range from 10% to 50%. The

volatilities of the two stochastic variables have significant impact on the shape of the

value surface of the swap. The value default-risky component of the swap decreases as the

rental volatility increases, which implies that the embedded premium that compensates the

bond-investors decreases as the uncertainty in the rental increases. The bond-holders

(fixed-rate receivers) are thus exposed to higher default risks associated with the floating-

rate payers in a high rental volatility environment. On the other hand, the default-risky

swap value is less sensitive to the risk-less interest rate uncertainty and the effects are not

discernible. The default premium of the swap decreases gradually when the interest rate

volatility increases from 5% to 20%. The default-risky swap component value increases

positively with the corresponding increases in the default-free interest rate volatility, only

when the volatility rises above 20%.


Figure 4.4: Present Value of Swap

In summary, the rental and risk-less interest rate volatilities are two important variables in

determining the value of the default risk in ABS deals. It is thus important to take into

consideration the dynamics of the securitized real estate rental and risk-less interest rates

when setting the equilibrium fixed-rates and floating-rates in ABS deals so as to mitigate

the likelihood of default. The model shows a negative relationship between the default-

risky component of the swaps and the rental cash flow (floating-rate) volatility. The

relationship between the default-risky swap premium and the default-free interest rate

volatility is relatively less sensitive. The default premium only increases positively in

relation to changes in default-free interest rate volatility when the volatility is above 20%.


4.6 Conclusion

Asset-backed securitization is a relatively new financial innovation in Singapore’s capital

market, which has been accepted by developers (originators) as an alternative source of

financing. Default risks have not been seriously examined for the ABS deals in Singapore.

Moreover, most of the ABS bonds issued till date were also not assessed by independent

credit rating agencies. The protection against defaults of the originator (floating-rate

payer) or the SPV (fixed-rate payer) is dependent solely on the credit worthiness of the

originator and the credit enhancer in the form of cash flow guarantee provided in some

ABS contracts. There is no attempt made thus far to explicitly quantify the default risks

associated with the ABS bonds. This study fills the gap in literature by proposing to

evaluate the credit risks of the ABS bonds using swap analytical frameworks.

The theoretical default-risky swap valuation models developed by Duffie and Singleton

(1999) and Hübner (2001) were adapted to value the default risks associated with the

originator and the SPV, and determine the equilibrium swap rate for the floating-rate and

fixed-rate payers in the ABS swaps. There are no analytical solutions available for the

model. The Monte-Carlo simulation technique is employed to provide numerical solutions

to the model. Using the Century Square shopping mall ABS case for illustration, the

numerical analysis results show significant effects of the changes in rental volatility and

default-free interest rate volatility on the default-risky component of the swaps. There is a

significant negative relationship between the rental volatility and the premium for default

risks in swap, whereas the relationship between the default-free interest rate volatility and

the swap default premium is positive only in the high volatility regions (above 20%). The


results suggest that the rental dynamics of the securitized real estate are critical in

determining the default risks in the ABS. The fixed-rate (coupon yield) and floating-rate

(rental cash flows) should be determined to adequately reflect the default risks that may be

caused by the rental dynamics of the securitized real estate.

Chapter 4

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