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  • Uberoi, Priya, 2010. “An Introduction to Islamic Derivatives,” Practice Note, Practice Law Company, March 25, Available at http://us.practicallaw.com/8-501-6191.

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  • Vogel, Frank E., and Samuel L. Hayes III, 1998. Islamic Law and Finance: Religion, Risk and Return (The Hague and Boston: Kluwer Law International).

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  • World Bank Group/Islamic Development Bank Group, 2017. “The Islamic Banking Sector,” Global Report on Islamic Finance (“Islamic Finance―A Catalyst for Shared Prosperity?”), Chapter 3, February 20 (Washington, D.C.: World Bank Group/Islamic Development Bank Group), 4767.

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Appendix I. Additional Tables

Table A1.

Glossary of Islamic Finance Terms for Banking

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Sources: authors, Errico and Farrahbaksh (1998), El-Hawary and others (2004), IFSB (2005a and 2005b), and ISRA (2010).
Table A2.

Stylized Balance Sheet of an Islamic Bank (with internally consistent values, in monetary units)

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Source: authors. Note: An electronic version of this table is available as MS Excel® workbook (“Datafile_Balance_Sheet_and_Output_Template”) which is published together with this working paper. 1/ trade financing; 2/ “special sales” are contracts with delayed settlement in the form of salam and istisna’a (delayed delivery) or bay bithaman ajil (delayed payment); 3/ assumption of 5 percent reserve coverage for UIA and RIA (see (17) and (18)); 4/ supervisory authorities may apply supervisory discretion to account for DCR also to RIAs; this would then change PER in (16) to include PERRIA (and a corresponding change of RWAs funded by reserves in (26) to include RWAs funded by PERRIA).
Table A3.

Output Template of Multiperiod Stress Test for an Islamic Bank—Main Results and Risk Drivers

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Sources: Jobst (2013b) and authors. Note: An electronic version of this table is available as MS Excel® workbook(“Datafile_Balance_Sheet_and_Output_Template”) which is published together with this working paper. PERUIA=profit equalization reserve for unrestricted investment accounts (UIA) and IRR=investment risk reserve. The values in the prepopulated cells are for illustration purposes only (but consistent with all the balance sheet items shown in Table A2).Sources: Jobst (2013b) and authors. Note: An electronic version of this table is available as MS Excel® workbook (“Datafile_Balance_Sheet_and_Output_Template.xlsx”) which is published together with this working paper.EAD=exposure at default, LGD=loss-given-default, PD=probability of default, NPA=nonperforming asset ratio, DCR=displaced commercial risk, PERUIA=profit equalization reserve for unrestricted investment accounts (UIA), IRR= investment risk reserve. The values in the prepopulated cells are for illustration purposes only (but consistent with Table A2).

The reporting basis can be either “solo” (legal entity level), “combined” (domestic operations and foreign branches), or “consolidated” (all group-wide activities, irrespective of jurisdiction and legal status (branches/subsidiaries));

The average PDs for the portfolio should be used to derive the asset correlation from the Basel II formula (by exposure types), which is then averaged across exposure types, weighted by EAD. The portfolio average PD includes both defaulted and non-defaulted exposures.

Appendix II. Modeling Unexpected Losses using the Extreme Value Theory

Relaxing the normality assumption of the distribution of investment returns in order to estimate unexpected losses requires estimating the tail risk. There are two practical approaches for determining the asymptotic behavior of investment returns under the extreme value theory (EVT): (i) the empirical calibration of the generalized extreme value (GEV) distribution and (ii) estimating the generalized Pareto distribution (GPD) as a subset of GEV based on exceedances.

A. Empirical Calibration Using the Generalized Extreme Value Distribution

We assume that the asymptotic tail behavior of a historical series of observations {xt; t = 1,2,..., n} with distribution function Ft (x) = Pr(Xt ≤ x) and x ∈ ℝ comprises a sequence of normalized extremes (maxima or minima) drawn from a sample of independent and identically distributed (i.i.d.) random variables based on the empirical observations specified in equation (B 1.1.) in Box 1; they converge to a GEV distribution as limiting law of their asymptotic tail behavior (reflecting the diminishing likelihood of even larger extremes as the level of statistical confidence approaches certainty).

The Fisher-Tippett-Gnedenko theorem (Fisher and Tippett, 1928; Gnedenko, 1943) defines the attribution of a given distribution of normalized maxima (or minima) to be of an extremal type. If the vector-valued i.i.d. random series

xt=x1,x2,xn,

we can define the sample maxima yx = max{x1, x2,..., xn) with ascending order statistics xτn,1xτn,n over n-number of observations.

The distribution of normalized extremes satisfies the conditions of the GEV distribution if there exists a choice of normalizing constants αxn>0andβxn>0, such that the probability of each ordered n-sequence of normalized sample maxima (yχαxn)/βxn>0 converges to the non-degenerate limit distribution Gyx (·) as n → ∞,88 so that

limzPr((yxαxn)/βxnx)Gyχ().

If the normalized extremes only roughly follow GEV, they are considered to fall within the maximum domain of attraction (MDA) of Gv (■). In this case, their distribution conforms to one of three distinct types of extremal behavior as limiting distributions (which are expressed below in their general form without specific notation):89

EV0:G0(x)=exp(exp(x))ifx0,ξ=0EV1:G1(x)=exp(x1/ξ)ifx[μσ/ξ[,ξ>0EV2:G2(x)=exp((x)1/ξ)ifx],μσ/ξ,],ξ>0.

If ξ > 0, GEV falls within the class of Fréchet (EV1) distributions, which feature regularly varying tails, including fat-tailed distributions, such as Stable Paretian distributions. ξ < 0 indicates (negative) Weibull (EV2)-type distributions, that is, distributions without a tail but a finite end-point (for example, uniform or beta distributions). In the case of ξ → 0, GEV approaches a Gumbel (EV0) distribution, which encapsulates thin-tailed distributions,90 for which all moments exist.

The cumulative distribution functions in the above equations are combined into a unified parametric specification of the GEV c.d.f, which for yx is defined as

Gyx(x)={exp((1+ξ(xμ)σ)1/ξ)if1+ξ(xμ)σ0exp(exp(ξ(xμ)σ))if x,ζ=0,(A2.1)

with the index for the test horizon dropped from this notation for simplicity. Differencing equation (8) above as Gyx'(x)=ddxGyx(x) yields the probability density function

gyx(x)=1σ(1+ξ(xμ)σ)1/ξ1exp((1+ξ(xμ)σ)+1/ξ),(A2.2)

where the scale, location, and shape parameters are estimated as μ^>0,σ^>0andξ^ respectively. The scale parameter represents the annualized volatility of returns. The shape parameter is determined by the type of sub-model (EV0, EV1, or EV2). The moments are estimated concurrently by means of the linear combinations of ratios of spacings (LRS) method, which determines how quickly the probability of extreme observations converges to zero, using the historical spread dynamics over a chosen estimation horizon (Coles, 2001; Jobst, 2007b). The associated maximum likelihood (ML) estimator is evaluated numerically by using an iteration procedure (for example, over a rolling window of a constant number of observations with periodic updating) to maximize the likelihood Πt=1ngyx(xt|θ) over all three parameters θ=(μ^,σ^,ξ^) simultaneously.91

Given the expectation

0xσ^(1+ξ^(xμ^)σ^)1/ξ^1exp((1+ξ^(xμ^)σ^)1/ξ^)dx=(μ^+σ^1ξ^)((1+ξ^(xμ^)σ^)1/ξ^)

based on the cumulative distribution function in equation (A2.1) above, we obtain the CTE (or conditional VaR) as probability-weighted residual density beyond a pre-specified “severity threshold” defined by VaRa,t with the statistical significance defined by the parameter a. Thus, equation (B1 .2) in Box 1 can be rewritten as

CTEa,t=𝔼[xt|xtGyx¯1(a)=VaRa,t]=μrUIAt+𝔼[zτ|zτGyx(1a)]σrUIA,

with quantile function

Gyx1(a)=μ^+σξ^^((ln(a))ξ^1)

and

VaRa,t=sup(Gyx¯1()|Pr(x>Gyx¯1())a).(A2.4)

Equation (A2.3) is specified by the general definition of CTE (Artzner and others, 1999) as

CTEa,t=VaRa,t(1Gyx(x))dx1Gyx(VaRa,t)=11aa1VaRa,tda.(A2.5)

B. Estimating the Generalized Pareto Distribution Using the Peaks Over Threshold Approach

Alternatively, the Peaks over Threshold Approach (POT) can be applied to approximate asymptotic tail behavior of all observations that exceed a pre-determined, sufficiently high threshold value.

We extract these extremes from the return distribution (see equation (B1.1) in Box 1) by taking the largest observations (exceedances) over threshold u, which is defined as xt > u for any t = 1,2,..., n. Given the right endpoint of x0 = sup{x ∈ ℝ: Ft (x) < l} ≤ ∞, the c.d.f. of excesses yt = xt – u is given by

Ft(y;u)=Pr[xtu<yt|xt>u]

for 0 ≤ xtx0u, which can be written as

Ft(y;u)=Ft(x)Ft(u)1Ft(u)(A2.6)

and approximated by the generalized Pareto distribution (GPD), whose c.d.f. is defined as

Hu(x)={1(1+ξ^(xu)σ^1/ξ^if1+ξ^(xu)σ^01exp(ξ^(xu)σ^)ifx,u𝔼,ξ^=0,(A2.7)

with quantile function

Hu1(a)=σ^ξ^(xu)((1a)ξ^1),(A2.8)

where the scale and shape parameters are estimated as σ^>0andξ^ respectively. We can rearrange equation (A2.6) above as92

Ft(x)=(1Ft(u))Ft(y,u)+Ft(u)(A2.8)

and replace Ft (y; u) with Hu(x) and Ft (u) with its empirical estimator n – nu/n so that the c.d.f.

FGPD,T(x)=1nun(1+ξ^yσ^)1/ξ^(A2.9)

if ξ^0, with the total number n of observations and the number nu of exceedances above the threshold u. The corresponding point estimate of Ft (u) < a for u = xt – yt can be derived from the corresponding quantile function

FGPD,t1(a)=u+σξ^^(nun(1a)ξ^1).(A2.10)

Thus, we can rewrite equation (B1.3) in Box 1 in terms of the quantile corresponding to the threshold choice so that

𝔼[zt|ztFGPD,T1(1a)]=FGPD,t1(1a)+𝔼[ztFGPD,T1(1a)|ztFGPD,t1(1a)].(A2.11)

Since the second term on the right is the average of the mean excess function (MEF)

e(u)=𝔼[Xu|X>u]=σ+ξu1ξ(A2.12)

over threshold quantile FtGDP(1a), which is linear in threshold u for 0 < ξ < 1 and σ + uξ > 0, we can write

𝔼[ztFGPD,t1(1a)|ztFGPD,t1(1a)]=σ+ξ[FGPD,t1(1a)u]1ξ.(A2.13)

Plugging equation (A2.13) into equation (A2.11) results in

𝔼[ztFGPD,t1(1a)|ztFGPD,t1(1a)]=FGPD,t1(1a)+σ+ξ[FGPD,t1(1a)u]1ξ=FGPD,t1(1a)+σξu1ξ.(A2.14)

Replacing equation (A2.11) of CTE above and equation (B1.3) in Box 1 with the expression above (equation (A2.14)), we have

CTEa,t=𝔼[xt|xtFt1(a)=VaRa,t]=μr˜UIAt+[FtGPD(1a)+σξu1ξ]σr˜UIA.(A2.15)

Appendix III. Modeling Displaced Commercial Risk via Contingent Claims Analysis

Displaced commercial risk (DCR) represents the share of unexpected losses that are not absorbed by holders of unrestricted investment accounts (IA) during times of stress (see Box 1). These liabilities are subject to the risk-sharing principle of shari’ah-compliant contracts and normally bear any shortfall in expected returns (or losses). Reserves (PER and IRR; see Figure 5) help mitigate the run-off risk by converting the equity-like claim of IA depositors, in whole or in part, into a quasi-secured credit claim. Despite the stability-enhancing characteristics of these reserves, transferring some shareholder wealth to unsecured creditors raises the bank’s default risk. In the firm value model, such as the Black-Scholes-Merton (BSM) approach, this conversion amounts to adding the outstanding amount of IAs subject to DCR to the amount of existing payment obligations, which raises the default threshold.

Contingent claims analysis (CCA) could determine a market-based estimate of DCR. CCA generalizes the BSM approach for the assessment of credit risk (Jobst and Gray, 2013), and helps estimate the fair value of reserves required to cover DCR as the marginal impact of a higher default threshold on the bank’s default risk over a pre-defined risk horizon. In CCA, this change of default risk would amount to higher market-implied expected losses of the bank due to a larger amount of outstanding liabilities relative to available assets using a risk-adjusted valuation of the balance sheet.

In general, CCA quantifies default risk based on the assumption that owners of equity in leveraged firms hold a call option on the firm value after outstanding liabilities have been paid off.93 The asset value is assumed to follow a random, continuous process and can be either above or below the amount required for the repayment of funding over a specified period of time. This capital structure-based valuation approach of state-contingent contracts implies default if a firm’s asset value is insufficient to replay non-equity investors (including depositors) at maturity, which constitutes the bankruptcy level (“default threshold” or “distress barrier”) in present value terms. Conversely, if the value of assets exceeds that of liabilities (that is, the “distance to default” is positive), the call option held by equity holders on firm value has intrinsic value (in addition to its time value until the maturity of debt).

The impact of DCR on expected losses can be valued as an implicit put option. The default risk is viewed if it were a put option written on the amount of outstanding liabilities, where the default barrier represents the “strike price,” with the value and volatility of assets determined by changes in the equity and equity options prices of the bank (or close approximations using various statistical techniques for non-listed banks, which are suggested in IMF, 2014). Since the repayment of all funds is considered “risky,” the probabilistic estimate of the default risk can be expressed as a put option on asset performance. The value of the put option value reflects the expected loss of the bank, that is, the probability and the degree to which the future asset value of the bank falls below the “default barrier.” It increases the higher the probability of the asset value falling below the default barrier over a predefined horizon. Such probability is influenced by changes in the level and the volatility of the implied asset value reflected in the bank’s equity and equity option prices, conditional on its capital structure, the maturity term of total payments to investors, and the leverage of the bank. The risk-adjusted return compensates for the expected losses investors accept in funding the bank (that is, the expected return on investment promised to IA holders).

The present value of market-implied expected losses can be priced as a (European) put option

𝔼t(Lt+τ)=PE(A,B,τ,t)=Φ(x)Bτ,terτΦ(x+)A˜t

if the change of the bank’s implied asset value over time, A˜t, is modeled as a geometric Brownian motion, where Φ(.) is the cumulative distribution function of the standard normal distribution, the present value D = Bτ,te-rτ of outstanding payment obligations B is the strike price on the asset value, asset volatility is defined as

σA˜=EtσEA˜tN(x+)=(1N(x)Bτ,terτA˜tN(x+))σE

over time horizon T – τ, with (observable) equity volatility, σE, market capitalization, Et, the risk-free rate of return, r, subject to the sensitivity

x±=1σA˜τ[lnA˜tBτ,t+(r±σA˜22)τ]

of the option price to changes in the relation between the implied asset value and all outstanding payment obligations after adjusting for asset volatility.

Thus, the (market-implied) estimate of the implicit transfer of shareholder wealth to UIA holders to cover DCR can be written as

ΔPE=PEDCR(A,B,DCR,τ,t)PE(A,B,τ,t),

which represents the impact of the non-mitigated impact of DCR on the (market-implied) expected losses of an Islamic bank,94 where

PEDCR(A,B,DCR,τ,t)=Φ(xDCR)(Bτ,t+DCRτ,t)erτΦ(xDCR+)A˜t,xDCR±=1σA˜τ[lnA˜tBτ,t+DCRτ,t+(r±σA˜22)τ],

and

DCRτ,t=α*×RWAUIARWAUIAUIAA,

95

based on the estimated unexpected losses according to the methodology in Box 1.

Appendix IV. The Process-Driven Perspective of Profits in Islamic Finance

The prohibition of interest-based forms of income under Islamic finance principles is inherently linked to the shari’ah concept of wealth (mal)96 The lawfulness of a transaction hinges on the commercial value of any obligation arising from the underlying contractual agreement. If an obligation is considered to have commercial value, it can be sold in exchange for another item of known value in return for fair compensation commensurate to the consumption of wealth. In this regard, two aspects are typically considered: (i) the nature of wealth and the defining elements of value in the Islamic legal tradition (al-fiqh); and (ii) the degree to which such value is realized in a transaction.97

Thus, the combination of the following three elements of wealth98 would make a transaction contractually valid (sakih) and permissible from a shari’ah perspective:99

  • The presence of an intended “usufruct” (that is, meaningful use). The meaningful use in the spirit of usufruct is defined as a proper objective in term of attracting a specific benefit or repelling detriment;

  • The commercial value of “usufruct.” If the object of a transaction is accorded value from a legal perspective, if it has generally acknowledged monetary value based on the commercial practice or current custom (al- ‘urf), this implies that the absence of wealth in the past bears no relevance to the current interpretation of wealth if customs as to the creation of value have changed over time; and

  • The lawfulness of “usufruct.” While the permissibility of any usufruct related to a contract requires the support of a legal (or scriptural) confirmation of its lawfulness, a similar prerequisite related to financial exchanges is neither sought after nor stipulated (Hammad, 2007). 100 Thus, the lawfulness of a contract—as a result of a financial transaction defined by the exchange of value for certainty about the value of a reference asset—depends on the underlying intent regarding its purpose and final use by the beneficiary rather than the general permissibility of the usufruct itself.

Appendix V. Comprehensive Representation of Credit and Market Risks in Stress Testing

The deterioration of a bank’s asset quality (due to either broad-based deterioration of economic conditions or a negative shock to a specific economic sector) results in a general increase of nonperforming asset (NPA) balances (and potentially higher specific provisions and charge-offs) and higher unexpected losses (which tends to be reflected in a higher capital intensity of credit-sensitive assets). While the realization of credit losses (and associated changes in expected losses) is relatively straightforward to measure and project, the change in capital intensity of unexpected losses, which can be expressed as

f(ΔPDportfolio)ΔRWAcreditΔPD+f(ΔHHIportfolio)ΔRWAcreditΔconcentration,(A5.1)

requires a detailed understanding of the sensitivity of credit RWAs to changes in default risk and portfolio concentration based on the historical credit performance and the composition of the bank’s credit portfolio.101

The following (additive) increase of risk weights can be considered using general assumptions about the sensitivity of RWAs under stress conditions:

  • The nonlinear effect of changes in PDs on RWAs, f(ΔPDportfolio), is determined by fixing the asset correlations to the lowest level of the PDs (that is, a level corresponding to an “AAA/Aaa”-rating) and the loss-given-default (LGD) to 45 percent.102 Thus, the marginal increase of RWAs (in percent) for an increase of PDs (in percent) can be calculated for each portfolio as (Jobst, 2013):

    ΔRWAcreditΔPD=0.12×ΔPDportfolio20.049×ΔPDportfolio+0.006,(A5.2)

    where the change in unexpected losses should be consistent with the change in loan loss provisions. The RWAs of total lending for a given level of PD (in percent) can be derived from

    RWA=K×12.5×EAD,(A5.3)
    K=LGD×[Φ(1/1R×Φ1(PD)+R/1R×Φ1(0999))PD](A5.4)

    and

    R=AVC×(0.12×1e50PD1e50+0.24×(11e50PD1e50))(A5.5)

    using the credit risk assessment for mortgage loans103 under the Basel III framework (BCBS, 2005). Φ(·) and Φ-1(·) denote the standard normal and the inverse standard normal cumulative distribution functions; EAD is the exposure at default; AVC is the asset value correlation (and takes the value AVC = 1.25 if the company is a large regulated financial institution [total asset equal or greater to US$100 billion] or an unregulated financial institution regardless of size, else AVC = 1). The estimate of forward-looking (expected loss) provisioning based on aligning loan loss provisions (relative to operating income) to the RWA-implied PD is (0.00092 x RWA2 – 0.06 x RWA + 1.662) x (LGD/100) (Jobst and Weber, 2016).

  • The impact of concentration risk on RWAs, f(ΔConcentrationportfolio), is calculated as the percentage increase of RWAs (in percent),

    ΔRWAcreditΔconcentration=100+(0.02+12.6×HHI),(A5.6)

    at portfolio level (HHI=Herfindahl-Hirschman concentration measure) for the average exposure-weighted default probability PDportfolio = 0.4%. For each 0.4 percentage point increase (PDportfolio > 0.4%), the value of ΔRWAcredit above increases by 1 + (PDportfolio/0.4% – 1) x 0.1; for instance, a very large portfolio with a low degree of concentration (HHI ≤ 0.0006) and an EAD-weighted PDportfolio = 0.8% would be expected to experience an increase of RWAs by 3.0 percent due to the impact of concentration risk on unexpected losses.

Similar to the consideration of unexpected losses from credit risk, higher price volatility and/or changes in the composition of listed exposures (sales and profit- and loss-sharing contracts) in the trading and investment portfolios (which are classified as MtM [or “held with a trading intent {HfT}”] and AfS [or”Fair Value Reported in Other Comprehensive Income {FVOCI}]” under the revised IFRS) change the unexpected losses from market risk, so that

ΔRWAmarket=f(ΔVaRportfolio)ΔRWAmarkeΔpriceRWAΔmarket.(A5.7)

The expression above reflects the change in the sum of VaR, stressed VaR, and incremental risk charges using short-term price changes over a 10-day period, f(ΔVaRportfolio) (consistent with the regulatory definition of market risk (BCBS, 2015)) and the net change in portfolio allocation affecting RWAs, RWAΔmarket, based on investment and trading behavior under stress.

Appendix VI. The Evolving Nature of Stress Testing

The effective implementation of stress testing approaches requires a framework that is relevant and adequate amid an evolving and complex international financial system. Greater data availability, enhanced statutory reporting, and supervisory coordination have also helped broaden the scope of macrofinancial linkages and their integration into more consistent scenarios, covering a wider range of non-bank financial institutions and markets. The IMF staff has made significant efforts to close important gaps that were highlighted by the global financial crisis to ensure that FSAP stress tests are fit for purpose and encompass the following four essential domains:104

  • Dynamic approach. A more dynamic approach considers changes in institutional behavior that can affect the capital impact of adverse macrofinancial scenarios. For instance, banks could react to stress situations by ringfencing liquidity, balance sheet adjustments (through asset sales and/or lower credit growth), raising capital, or withholding dividends;

  • Spillover effects. The interconnectedness within financial systems (such as interbank markets) and the interactions of financial institutions with non-financial entities (through common exposures, such as the housing market), both within and across national boundaries, can result in knock-on effects related to financial contagion and amplify initial shocks system wide;

  • Cross-functional perspective of solvency and liquidity risks. Liquidity and solvency risks of individual institutions are increasingly connected during times of stress and tend to be influenced by system-wide liquidity conditions associated with the interconnectedness and network effects within the financial system.105

  • Feedback loop with real economy. The two-way interaction between the real economy and financial activities, and related feedback effects generated by banks’ reaction function to stress requires a dynamic specification of transmission channels (including the consistent and comparable design of macrofinancial scenarios, which could be enriched with insights into the adjustment process of economic agents to price and output shocks from full (or partial) equilibrium macroeconomic models).

1

Corresponding authors: Andreas (Andy) A. Jobst, European Department; Juan Solé, Monetary and Capital Markets Department. We are grateful for comments from Marco Espinosa, Giancarlo Gasha, Abdullah Haron, Maher Hassan, Jad Khallouf, Divya Kirti, Mindaugas Leika, Abozer Majzoub Mohammed, Mohamed Norat, Ghiath Shabsigh, Zeine Zeidane, and an anonymous reviewer from the Bank Negara Malaysia, as well as attendees of the departmental QUANTM Seminar (July 2019) and a workshop on Islamic bank stress testing, which was organized by the Istanbul School of Central Banking in June 2019. We thank Cathy Lips and Lilly Siblesz de Doldan for their editorial support.

2

Readers may consult the IMF’s COVID-19 website, which includes a tracker of key policy measures and staff recommendations with regard to the CO VID-19 global outbreak as well as a current analysis of financial stability implications in the April 2020 issue of the Global Financial Stability Report (IMF, 2020a).

3

On the supply side, production, trade and travel disruptions are slowing the delivery of intermediate goods and foreign labor/expertise in EMDEs that are tightly integrated into global supply chains. On the demand side, commodity exporters and those countries with large tourism sectors suffer from a deterioration of their terms of trade, further exacerbating the contraction domestic real activity.

4

The conventions of Islamic finance are particularly suitable for infrastructure development. The asset-backed and project-specific nature of Islamic finance structures and their emphasis on risk sharing make them a natural fit for public-private partnerships in infrastructure development. Islamic finance can be flexible, as reflected in the wide variety of structures that are available to those who want to either (1) finance the purchase of land and equipment to build assets; or (2) lease assets upon completion and pay for their use (Levy and Iqbal, 2018).

5

Despite the bank dominance in Islamic finance, long-term institutional investors and market-based finance are becoming quite relevant. About one quarter of shari’ah-compliant financial services are attributable to capital market activities, insurance (takaful or ), microfinance and other nonbank finance (such as investment funds, captive financial institutions and money lenders as well as broker-dealers), and financial auxiliaries.

6

The IFSB (2018) currently considers the Islamic financial sector systemically important in 12 countries (Bahrain, Bangladesh, Brunei, Djibouti, Iran, Jordan, Kuwait, Malaysia, Qatar, Saudi Arabia, Sudan, and UAE). Yemen also qualifies based on the current size-based criterion of systemic relevance but was not included due to data constraints.

7

The other countries among the largest Islamic banking jurisdictions are Bahrain, Bangladesh, Indonesia, Qatar, and Turkey (IFSB, 2018).

8

For a recent assessment of the performance and regulation of Islamic banks, see World Bank/Islamic Development Bank Group (2017).

9

The availability of strong regulation and supervision is a key factor of assessing system-wide vulnerabilities of the capital adequacy of countries’ banking systems to various risks. The IFSB introduced two standards, capital adequacy requirements (IFSB, 2005a and 2013) and risk management practices (IFSB, 2005b), which are particularly relevant for the capital assessment of Islamic banks under stress (Kammer and others, 2015).

10

Well-formulated stress tests comprise different methods, such as sensitivity and/or scenario analyses, to assess the overall capacity of an individual bank or the entire banking sector to absorb shocks from the realization of key macrofinancial risks. They can also provide a cross-sectoral perspective by capturing the interconnectedness of banks, insurers, and other market participants.

11

The IMF has made it mandatory for 29 jurisdictions with systemically important financial systems to undergo FSAP assessments every five years. These include all FSB member jurisdictions, except Argentina, Indonesia, Saudi Arabia, and South Africa, which are G-20 member countries. FSAP stress tests attempt to cover all relevant sources of risk affecting the performance and capital and liquidity risk assessment of the financial system. The outcomes of stress tests are driven by the initial identification of these risks in detecting, monitoring, and mitigating buildup of risks based on known vulnerabilities from common exposures, risk concentrations, and interdependencies across the financial system.

12

A common metric of risk factors and shocks allows for an integrated analysis at a system-wide level in mixed banking systems. However, the capital impact of a given scenario defined by changes in economic activity, asset prices, and interest rates/rates of return is likely to differ between conventional and Islamic banking activities under stress. Supplementary sensitivity analyses can usually provide additional insights and help identify how these outcomes can be explained by the differential impact of risk drivers.

13

Solvency stress tests remain focused largely on credit and market risks (for example, interest rates, exchange rates, and credit spreads as well as equity and commodity prices).

14

The scope of the paper is limited to Islamic banks and is aimed at both the institutional level and system-wide stress tests; however, elements of the paper can be readily applied to stress testing “Islamic window” operations of conventional banks, which are self-contained.

15

The IFSB (2016) also covers liquidity stress testing in its recent guidance note. For a conceptual overview of liquidity stress testing, see Jobst and others (2017).

16

Note that the capital standard for Islamic financial institutions is in the process of being revised to align several of its elements to the finalized Basel III framework and the International Financial Reporting Standards (IFRS).

17

Shari’ah-compliant financing contracts substitute the profitable sale of assets for the permanent transfer of funds at a specified interest rate (underpinning the “self-generating” profit proposition in conventional finance) (Subhani, 2011). In practical terms, the principle of permissibility under Islamic finance principles is generally taken to mean that profits from bilateral exchanges are considered shari’ah-compliant (and serve a public good in a general sense (maslaha or )) in the absence of a clear and specific prohibition through religious censure (taqlid or ) (Uberoi, 2010).

18

Riba is generally understood as the realization (or prospect) of an economic advantage through excessive compensation, which can occur either (i) as “usury in trade” in the form riba al-buyu when two or more species (anwar or ) of the same genus (jins or ) are exchanged in unequal quantities in a spot sale (riba al-fadl or ) or with deferred delivery (riba al-nasi’a or ), subject to the same efficient cause (illah or ), or (ii) as “usury in debt” in the form of riba duyun , which defines an unjustified increment in money lent over and above the principal amount at the point of contract (riba al-qur’an or ) or for late repayment or failure to repay the loan (riba jahiliyyah )or hus, Islamic finance principles prohibit profits from exchange-based contracts of the same goods and/or services at different prices (or quantities) between buyer and seller (bay al-inah) or with delayed payment. This practice extends to the trading of debt (or promises) with debt (bay dayn bi-dayn) at a price different than its face value (regardless of whether the transaction occurs spot or in the future).

19

Note that the Shari’ah Advisory Council (SAC) of Bank Negara Malaysia (BNM, 2010) determined that the application of time value of money principle is permissible for exchange-based contracts with deferred payment since the seller sacrifices the present consumption of money due to the delayed payment, and, thus, limiting the scope of riba al-nasi’a (or ). However, this assessment does not affect the prohibited compensation for time in loan contracts (riba al-qur’an or ).

20

The general consensus among Islamic scholars is that riba covers not only usury but also the charging of interest and any guaranteed rate of return regardless of the performance of an investment or granted benefit (Iqbal and Tsubota, 2006). Thus, the process-oriented view of generating return in shari’ah-compliant investment aims at mitigating the risk of exploitation from passive income.

21

The delayed delivery or payment is permissible if its commercial value (“diversity of trade”) overrides term contingencies, such as in the case of salaf (forward trade or ), which restricts any contingency risk limited to predefined timing mismatch of delivery or payment.

22

Note that interest rate risk is equivalent to the change in the cost of funding relative to the expected return from shari’ah-compliant investment/lending in response to changing monetary conditions affecting Islamic banking.

23

See Solé (2008) for a discussion of requirements for conventional banks that offer Islamic finance products.

24

Many Islamic banks have limited access to central bank liquidity and lack sufficient long-term funding, which makes them structurally vulnerable to funding shocks. In most cases, liquid (but expensive) short-term assets and illiquid (but profitable) long-term assets are funded by short-term deposits, investment accounts, and, to a lesser extent, long-term exchange-based/profit- and loss-sharing contracts. The risk from a “long-short mismatch” is exacerbated by the underdeveloped inter-bank money market in shari’ah-compliant instruments.

25

Conventional banks generally benefit from rising interest rates as long as they can pass on higher funding costs to borrowers so that their net interest income at least offsets the lower valuation of fixed income investments through the profit and loss statement.

26

Note that the recognition of capital instruments for regulatory purposes is complicated by the principle of subordination arising in both equity-based and exchange-based contracts when used for structuring additional Tier 1 and Tier 2 capital instruments supplementing common equity Tier 1 capital (which is the subordinated claim to a bank as a gone concern). Sairally and others (2013) suggest musharakah sukuk for additional Tier 1 and convertible murabahah or ijarah sukuk for Tier 2 instruments to achieve the effect of subordination among qualifying capital instruments relative to depositors and general creditors of an Islamic bank.

27

However, in some countries, such as Malaysia, investment accounts represent only a small portion of total funding, which is dominated by deposits in the form of current accounts and reverse sales. For instance, UIAs account for less than five percent of total funding of Islamic banks in Malaysia.

28

While UIAs are loss-bearing in principle, there is an expectation that some losses are cushioned by reserves, creating so-called displaced commercial risk (DCR).

29

IAS 32 specifies the presentation for financial instruments according to the IFRS. For presentation, financial instruments are classified into financial assets, financial liabilities, and equity instruments. The differentiation between a financial liability and equity depends on whether an entity has an obligation to deliver cash (or some other financial asset).

30

See Iqbal and Mirakhor (2006) for a short description of these instruments. Note that in Malaysia, also UIAs do not guarantee the full repayment of principal and return.

31

Both types of equity-based contracts are considered profit- and loss-sharing. However, in a mudarabah contract (similar to a general and limited partnership), the financier (rabb-ul-mal) provides all of the funding while the entrepreneur (mudarib) provides specialized knowledge in managing the investment project without making a financial contribution. Thus, any capital losses accrue to the financier whereas the entrepreneur will incur the opportunity cost of the time and effort invested in the project. Hence, only the musharakah (joint-venture) is genuinely profit- and loss-sharing from a financial perspective. The same distinction applies to the use of these contracts in the funding structure of Islamic banks (see Table 1).

32

Conversely, the bank (borrower) could also defer all (or some) payment (bay bithaman ajil) for receiving the contracted asset from the borrower (bank).

33

In a reverse murabahah (or tawarruq) contract, which follows the same process but does not involve a specific asset to be financed, the bank purchases a commodity from a third-party on credit at a higher price to obtain liquidity by selling it again in the market.

34

For example, the bank may acquire and carry the asset on its balance sheet for a short period of time so that it can complete a murabahah contract by selling it again.

35

Full loss-sharing occurs under musharakah contracts, whereas under mudarabah contracts, all losses are borne by the lender.

36

Notice that this definition also applies to sukuk held for trading and “conventional equity” positions (that is, equity issued by firms whose operations and output follow conventional finance principles but would be eligible for investors that are bound by shari’ah principles). Thus, these positions are not necessarily open-ended, but can have a certain maturity date.

37

For example, murabahah transactions are increasingly realized via the purchase and sale of agricultural commodities like cocoa, rice, cotton, and maize. However, in many countries, the market volume of transactions (and the resulting inventory) underlying these Islamic contracts outstrips the real demand, which exposes Islamic banks to considerable commodity price risk.

38

See Greuning and Iqbal (2008) for a more detailed discussion of risk analysis in Islamic banking.

39

The dependence on holding inventory of commodities as generic collateral for most financial transactions limits asset diversification.

40

This is often referred to as rate of return risk (and indirect interest rate risk in mixed banking systems).

41

The liquidity stress testing work stream of the Basel Committee’s Research Task Force (RTF) found that disregarding the interaction between funding costs and solvency can cause the impact of standalone liquidity or solvency stress tests to be underestimated by between 30 and 50 percent under standard adverse scenarios (BCBS, 2015).

42

Note that the loss-bearing capacity would be contractually limited to loss- and profit-sharing (musharakah) contracts.

43

IAs also raise unique consumer protection issues because of inadequacies in disclosures and the asymmetric treatment of IAs as investors without shareholder rights (Lukonga, 2015).

44

For example, consider the case of an Islamic bank that accepts IA deposits via mudarabah (profit-sharing) contracts and invests the funds in long-term murabahah and ijara contracts (ordinary sales with fixed return). However, the bank realizes returns that may be lower than what was anticipated when the initial investment was made. In this case, mudarabah investors might be inclined to withdraw their deposits.

45

This way they reduce the probability of some shareholder value being transferred to IA holders during periods of underperformance. See also IFSB (2010) for a discussion on smoothing techniques for IA holders, which is complementary to the one presented in this paper.

46

Existing IA holders hold no legal claim on either type of reserves. If an account is closed, the prorated amount of reserves becomes orphaned, and banks may donate them to charity. However, this practice requires high standards of corporate governance to ensure that the management and accumulation of these reserves is transparent.

47

However, since these contracts are partially (or fully) collateralized, credit risk in Islamic finance contracts is mitigated by the collateral value after accounting for the market liquidity risk, which is the risk that it will not be able to sell an asset quickly (due to a deterioration of its liquidity value) without materially affecting its price.

48

Islamic banks undertaking the parallel salam transaction are exposed to credit risk in the event that the purchaser fails to pay for the commodity it had agreed to purchase from the Islamic bank. Nevertheless, in the event of non-delivery of the commodity by the seller under the initial salam contract, the Islamic bank is not discharged of its obligation to deliver the commodity to the purchaser under the parallel salam contract.

49

Note that such market risk does not apply to parallel contracts on special sales with deferred payment (bay bithaman ajil) since commodities would have been delivered already. However, parallel bay bithaman ajil contracts, which involve a delayed payment by the bank to a third party and thus help them manage liquidity more efficiently, are also affected by additional credit risk. A depreciation of the asset price of the commodities increases the probability of non-payment, which could create additional funding needs at maturity.

50

See Jobst and Solé (2009 and 2012) for discussions on hedging possibilities within the context of Islamic finance.

51

For a detailed definition of operational risk in Islamic banking, see IFSB (2005a and 2005b).

52

Where the funds are commingled, the RWAs are calculated based on their pro-rata share of the relevant assets funded by IAs, including PER and IRR, or equivalent reserves.

53

Since these potential losses may be hard to measure in practice (Jobst, 2007a), the IFSB adopted the Basic Indicator Approach (BIA) of the Basel framework for regulatory treatment of operational risk. Under the BIA, the capital requirement for operational risk is equal to the average over the previous three years of a fixed percentage of positive annual gross income. The recommended percentage is 15 percent (IFSB, 2005a).

54

The inclusion of reserves as part of eligible capital is not uniform across countries with substantial Islamic banking activity (and would exclude reserves to cover expected losses of UIA holders). For instance, in Bahrain, PER and IRR are included in regulatory capital as Tier 2 capital “up to a maximum amount equal to the capital charge pertaining to 30 [percent] of the risk[-]weighted assets financed by unrestricted investment account holders (Central Bank of Bahrain, 2008, Section CA-2.1).”

55

For instance, in the case of Malaysia, the market and credit RWAs attributable to investment accounts are excluded from the capital requirement. In addition, these investment account holders are not protected by deposit insurance.

56

Conversely, the application of DCR implies that affected IAs are explicitly excluded from the financial safety net (that is, deposit protection scheme) of the relevant jurisdiction.

57

The IF SB (2011) issued a Guidance Note providing further details on how to calculate this parameter to encourage consistency in the cross-country treatment of reserves for capital adequacy purposes and used a parameter value of 30 percent as an example, which, for instance, has been chosen by the Central Bank of Bahrain (2008). See also Iqbal and Mirakhor (2006) for a discussion on the choice of the α-parameter.

58

However, note that any musharakah-based RIAs imply profit- and loss-sharing, so a share of RIA also has a loss-absorptive capacity (which is generally not reflected in the capital assessment). For simplicity, we do not recognize this aspect of loss absorption in the denominator of CAR.

59

So RWAtotal includes αRWAUIA and the (1 – α) share of RWAs funded by PER and the share of IRR available to cover UIAs, which are subject to DCR. Thus, αRWAUIA represents the maximum value of DCR.

60

In general, the consideration of loss absorption in the capital adequacy formula for Islamic banks would require that loss-absorbing IAs are excluded from deposit insurance and IA holders fully accept investment risks and are able to bear losses, which remains untested in practice.

62

Since the volatility of returns tends to be higher after negative returns (Black, 1976) the asymmetric power ARCH (or AP ARCH) model defines the conditional volatility of returns as σtδ=α0+α1(|εt1|γεt1)δ+βσt1δ, with α, β, γ > 0 and α0 > 0, where -1 < γ < 1 captures the leverage effect, δ is the power, and εt = σt zt with zt following a standard normal distribution.

63

The exact category names may differ depending on the local accounting rules used in each jurisdiction. For instance, International Financial Reporting Standard 9 (IFRS 9) of the International Accounting Standards Board (IASB) does not use this nomenclature. Roughly speaking, MtM corresponds to “held with a trading intent” (HfT), AfS corresponds to “fair value reported in other comprehensive income” (FVOCI), and HtM corresponds to “fair value through profit and loss” (FVPL) at amortized cost. However, U.S. GAAP continues using these categories (under Accounting Standard Codification [ASC] 320). In Islamic finance, AfS exposures are often called “available for lease” (AfL), which acknowledges their functional characteristics for exchange-based contracts.

64

Operational risk losses are inherently difficult to model within the context of changing macrofinancial conditions and would require a specific calibration. In most cases, operational risk losses are held constant (unless some cyclical aspects of operational risk exposure, such as internal and external fraud, are considered in more detail).

65

Satellite models are essential to the stress testing framework, which includes (i) the object of analysis (structural conditions, regulatory situation); (ii) the determination of coverage (single entity or consolidated reporting); (iii) the development of a methodological framework (and analysis of data quality); (iv) considerations regarding the accounting standard and the treatment of capital resources; (v) the design of stress scenarios (single period versus multiple period, aggregate versus joint effects (after considering diversification); (vi) the definition of output measures; (vii) the validation of results; and (viii) dealing with the outcome of the stress test (Jobst and others, 2013).

66

Financial guarantees are considered shari’ah compliant only if they are directly related to the funding for the completion of a service or the production of a good.

67

This scenario can also be interpreted as a liquidity risk shock.

68

Note that specification of retained earnings in equation (8) excludes any investment shortfall that exceeds reserves. Instead, such net investment shortfall is shown separately for illustrative purposes.

69

Note that indirect interest rate risk refers to an ex post adjustment to a pre-defined rate of return and does not imply that Islamic banks are generally unable to adjust profit rates; in fact, in countries with a mixed financial system, such as Malaysia, where exchange-based funding liabilities, such as reverse murabahah contracts, have evolved into the dominant form of deposit funding, Islamic banks adjust their profit rate by offering new fixed deposit with a different profit rate in response to changes in monetary policy, just like their conventional peers (see Table 1).

70

Estimating the effect of changes in conventional banks’ interest rates on the depositors’ base of Islamic banks is an important but underexplored research area for which longer time series than currently available are needed.

71

The specification of retained earnings in equation (12) excludes the interest rate gap that is not absorbed by reserves on the calculation of net operating profits after taxes and dividend payouts. Instead, the interest rate gap is shown separately for illustrative purposes.

72

Credit losses are typically forecast based on separate models for write-downs and write-ups specific to each sector (corporate, retail, public, and financial institutions) or even more granularly, each portfolio under these sector headings. A simpler approach could also be applied by computing net losses.

73

Credit risk shocks affecting the valuation of financial market instruments tend to be implemented via a rating class-specific widening of credit spreads based on historical calibration. These shocks assume an increase in default risk but not a general change in the rate of return impacting the valuation of all investments.

74

The specific provisioning under IFRS 9 is based on accounting rules (“credit risk approach”) using (forward-looking) estimates of the probability of default (PD) and loss-given-default (LGD) to calculate expected losses on the book value (that is, historical [amortized] cost) of the exposure. Under the previous accounting standard (IAS 39), backward-looking PD and LGD were used to calculate incurred losses as a measure of expected losses. The credit risk parameters (PD and LGD) for the calculation of regulatory capital requirements could differ from those applied in statutory reporting (that is, financial statements) based on prevailing accounting standards.

75

The amount of specific provisions should not include accrued returns on missed payments (unlike conventional banks’ reporting under IFRS, which allows accrual of interest income on NPAs). Accrual accounting assumes that income is recorded in the period earned rather than in the period of the cash flow; however, interest accruals can distort financial reporting due to the following issues: (i) lending income is recorded even though the borrower does not repay; (ii) NPAs increase from the accrual at the rate of uncollected repayment; and (iii) provision coverage loses meaning since there is a matching provision to accrued returns.

76

This equation can be further refined based on the changes in the “automatic” collateralization of many shari’ah-compliant contracts due to the requirement of direct investor claims to the profit-generating asset/capital.

77

Stress testing of expected losses from credit risk that are in line with current accounting approaches are explained in Gross and others (IMF, forthcoming).

78

Note that this expression could be refined by conditioning the marginal increase of RWAs for credit risk on share of RWAs for credit risk (not total RWAs) funded by investment accounts (RIA and UIA).

79

Therefore, the resulting impact on capital adequacy provides a lower bound (or a worst-case impact) for this particular shock.

80

This excludes equity-based transactions (musharakah/mudarabah), which do not involve any form of collateralization by definition.

81

See Blaschke and others (2001) and Čihak (2007) for a detailed explanation of how to approach foreign exchange risks. See also IFSB (2005a).

82

This dimension of market risk is an important consideration when modeling shocks to the credit risk of special sales and establishes an important link between credit and market risk. In fact, the capital standard for Islamic banks distinguishes between single salam contracts and salam contracts with parallel salam contracts in setting risk weights (IFSB, 2005a).

83

Thus, shocks in stress tests are frequently informed by structural (predictive factor) models based on key risk indicators (KRIs) as a way of blending both quantitative and qualitative approaches that go beyond the exclusive regulatory treatment via a separate capital charge.

84

In fact, capital adequacy for operational risk appears incidental to the importance of corporate governance paired with suitable risk management and control procedures.

85

The simple aggregation of risk factor impacts would preserve the stochastic assumptions of each risk factor.

86

Although there are some deviations (mostly related to granularity of exposures), in general, this toolkit is broadly consistent with current capital requirements and accounting standards.

87

See also Adrian and others (2020) for review of current IMF stress testing approaches.

88

The upper tails of most (conventional) limit distributions (weakly) converge to this parametric specification of asymptotic behavior, irrespective of the original distribution of observed maxima (unlike parametric VaR models).

89

See Embrechts, Klüppelberg, and Mikosch (1997), Coles (2001), Vandewalle, Beirlant, and Hubert (2004), as well as Thérond and Ribereau (2012) for additional information on the definition of EVT.

90

For instance, normal, log-normal, gamma, and exponential distributions.

91

Note that the maximum likelihood estimator fails for ξ ≤ -1 since the likelihood function does not have a global maximum in this case. However, a local maximum close to the initial value can be attained.

92

Note that the specification of the GEV and GPD probability distributions assumes stationarity; however, in practice, extreme observations often violate the stationarity assumption. If the stochastic process of asset returns is non-stationary, the estimated parameters are time-dependent. See Cheng and AghaKouchak (2014), Cheng and others (2014), Ruggiero and others (2010), and Chavez-Demoulin and Embrechts (2004) for alternative approaches to deal with non-stationarity in extreme observations.

93

It is based on three principles: (1) the values of liabilities are derived from assets; (2) assets follow a stochastic process; and (3) liabilities have different priorities (senior and junior claims).

94

Note that this approach uses market prices to endogenize the risk-weighting of assets in the market-based assessment of solvency risk, and thus the impact of DCR on the scope of loss-absorption through the liabilities funding assets that experience a negative valuation shock (that is, losses from projects [investments and lending] undertaken by the bank).

95

Note that the uncertainty around DCR could also affect the implied asset volatility, aA, which is kept constant for simplicity.

96

See Kammer and others (2015) for a conjunctural perspective on Islamic finance.

97

The assessment of whether a transaction is permissible tends to follow shari ‘ah rulings (ijtihad) aimed at determining its “effective cause” (illah) based on analogous reasoning (qiyas). However, this purely legal perspective based on historical precedent could result in a very restrictive legal interpretation of shari’ah principles, suggesting a greater focus on the original objective and intent of Islamic contracts (maquasid al-shari’ah) based on economic rationale (hikmah).

98

More specifically, a legal definition of wealth is stated in Al-Buhuti (2003) as “whatever has a legitimate usufruct for other than a needs-related interest or a [life-saving] essential,” which excludes whatever is without use or has illegitimate use as well as permitted use in exceptional circumstances or for specifically defined purposes.

99

As further aspects of the concept of wealth creation, shari ‘ah also prohibits betting and gambling (maisir) as unethical (or socially detrimental and sinful) activity (haram) in contracts with a remote probability of positive payoffs to the investor (“game of chance”) and preventable contractual uncertainty (gharar).

100

Ahmad (1949) states that lawfulness is precedent in all financial contracts and transactions unless there is clear a prohibition. This is further clarified by Al-Shawkani (1984), who stated that “anything to which a lawful usufruct may be attributed may lawfully be sold. However, anything which has no usufruct to begin with (or which has an unlawful usufruct) may not be lawfully sold. This is because the means to the unlawful is itself unlawful.”

101

This equation can be further refined based on the changes in the “automatic” collateralization of many shari’ah-compliant contracts due to the requirement of direct investor claims to the profit-generating asset/capital.

102

Since the impact of LGDs on RWAs is linear, the elasticity of unexpected losses leading to changes in RWAs can be extracted from the Basel II IRB formula for corporate loans.

103

Due to the frequent absence of granular data on the maturity profile of lending contracts, this simplified approach was chosen (with loss of generality).

104

Dees and others (2017) present the models supporting the EU-wide stress testing exercises as part of an overall framework that covers a similar set of principles and concepts governing the key dimensions of macroprudential stress testing.

105

The assumed origin of the stress is usually an adverse shock to the credit portfolios of banks, which affects the risk drivers (PDs, LGDs) and/or asset values. These first-round shocks reduce the capital ratio. If capital becomes a binding constraint, liquidity risk emerges in various forms in most models. A declining capital ratio can lead to higher funding costs, charged by lenders as a reflection of higher counterparty risk. Liquidity risk can also follow from feedback effects arising from various transmission channels. Some models assume that funding rollover stops in response to higher counterparty risk and defaults in the network of exposures.