nacaskul, poomjai (2006), “survey of credit risk …€¢ credit derivatives, e.g. credit default...

Nacaskul, Poomjai (2006), “Survey of Credit Risk Models in Relation to Capital Adequacy Framework for Financial Institutions”, [http://papers.ssrn.com/abstract=1625254].

Nacaskul, Poomjai (2006), “Survey of Credit Risk Models in Relation to Capital Adequacy Framework for Financial Institutions”, [http://papers.ssrn.com/abstract=1625254].

Credit Determinant Models

a. Discriminant Analysis–based

i. Linear Discriminant Analysis – linearly separable feature space

ii. Support Vector Machine – (non)linearly separable feature space

b. Regression Analysis–based

i. Binary (Logit/Probit) Regression – linear, parametric estimation/classification

ii. Artificial Neural Networks – nonlinear, semi-parametric estimation/classification

Rating Transition Models

c. Discrete-Time Finite-State Transition

i. Stationary Markov Chain (MC)

ii. Nonstationary/Time-Heterogeneous MC

iii. Non-Markov Process (w/ Persistence of Memory)

d. Continuous-Time Finite-State Transition

i. Continuous-Time Markov Process

ii. Stochastic Transition Intensity Model

Default Process Models

a. Structural Default (Asset-value) Models

i. Merton’s Asset-value Model

ii. Black & Cox’s First-Passage Model

iii. PD Calibration vs. Historical Default Data

b. Default Intensity (Reduced-form) Models

i. Forward Default Intensity/Hazard Rate Model

ii. Doubly Stochastic/Stochastic Default Intensity Model

Credit Portfolio Models

c. Default/Rating Transition Correlation Approaches

i. Bernoulli Mixture Approach

ii. Multivariate Normal Approach

iii. Distributional Copula Approach

d. Stochastic Arrival/Loss Convolution Approaches

i. Poisson/Renewal Arrival Process

ii. Mixed Poisson/Negative Binomial Counting Process

iii. Extreme-value Losses/Sub-exponential/Heavy-tailed Distributions

พมใจ นาคสกล (๒๕๕๓), “เผย(หว)ใจ Basel II – IRB Risk Weight Function”, [http://www.bot.or.th/Thai/FinancialInstitutions/New_Publications/QMFE/Folder2/Pages/RelatedArticles-Others.aspx].

// สถาบนการเงน > เอกสารเผยแพร/สNงพมพ > แบบจาลองเชงปรมาณและวศวกรรมการเงน //

P O O M J A I N A C A S K U L , P H D , D I C , C F A

quantitative RISKMANAGEMENT analytics

M a y 2 0 1 3

F S V P , Q u a n t i t a t i v e M o d e l s a n d E n t e r p r i s e A n a l y t i c s

S i a m C o m m e r c i a l B a n k P L C [ P o o m j a i . N a c a s k u l @ s c b . c o . t h ]

quant RISK MANAGEMENT analytics

• Part I – Risk Management Fundamentals

• Part II – Market Risk

• Part III – Credit Risk

• Part IV – Operational Risk

• Part V – Residual, Hybrid & Non-Probabilistic Risks

(I.A) Risk Definition

• (Knightian) Uncertainty = Possibility; Utility

• e.g. coin landing ∈ ‘Head’, ‘Tail’

• Risk = Uncertainty, Probability; Utility

• e.g. coin landing ∈ ‘Head’, ‘Tail’ s.t.

P(‘Head’) = 1 – P(‘Tail’) = 0.6U(‘Head’) > U(‘Tail’)

• Informal: “chance of something bad happening!”


• Financial Risk ⇐ when ‘risk’ becomes ‘financial’

• Outcomes monetarily valued/priced

• Randomness due to financial/economic variables

• Intrinsic to financial markets/institutions,

• Mitigated by financial tools/instruments

• Risk Management = Process

• Identify Measure Mitigate Report …


• Market Risk• opportunity/possibility & probability

of financially relevant gains/losses due to ‘movements’ of the financial-marketand monetary-economic variables, • namely interest/exchange rates,

equity/commodity prices, etc.

• “Risk is business.”


• Credit Risk• opportunity/possibility & probability

of financially relevant losses (occasionally gains) due to ‘credit events’:

• For bank loans: obligor default, recovery, drawdown risks, respectively, PD, LGD, EAD; counterparty/settlement risks.

• For defaultable bonds: default + rating-downgrade risks.

• For credit derivatives: single-obligor events (i.e. CDS & CLN pricing); multi-obligor events (i.e. basket CDS & CDO pricing), etc.

• “Risk is compensated vis-à-vis business.”


• Operational Risk• opportunity/possibility & probability

of (partially) preventable occurrences of failures, errors, frauds, together with noncircumventable events in the form of random accidents, natural catastrophes, man-made disasters, • whence resulting in material losses, disruptions,

and/or various infractions, thereby severely and adversely impacting financial condition, business conduct, and institutional integrity overall.

• “Risk just for being in business.”


• On the nature of ‘risk ownership’

• Market Risk – specific to financial instruments and exposures ⇒ very localised ‘risk ownership’

• Credit Risk – characterised by chains of liability exposures ⇒ somewhat localised ‘risk ownership’

• Operational Risk – characterised by negative externalities ⇒ broad, enterprise-wise ‘risk ownership’


• On the nature of ‘risk arrivals’

• Market Risk – variables in continuous existence

• Credit Risk – hybrid mixture of discrete arrivals& continuous processes

• Operational Risk – discrete, scenario-driven events


• On the nature of ‘risk variables’

• Market Portfolio – finite sum of continuous random variables

• Credit Portfolio – finite sum of discrete-conditional continuous random variables

• Operational Portfolio –infinite sum of discrete-conditional continuous random variables.

III. CREDIT RISK

• 3A – Credit Risk: ‘Parsed’ Definition

• 3B – Single-Obligor Defaults, Loss Distribution

• Modelling Credit Obligor Risk

• 3C – Default Correlation, Credit Portfolio Models

• Modelling Credit Portfolio Risk

• 3D – Regulatory Capital vs. Economic Capital

• 3E – Credit-Sensitive Assets, Credit Derivatives

(III.A) Credit Risk: ‘Parsed’ Definition

• opportunity/possibility & probability of losses(occasionally gains), particularly in the form of:

• Credit Obligor Defaults & Credit-Sensitive Assets, i.e. Bonds

• Exposure At Default = Principal + Interest

• Probability of Default ⇒ Default Event, D ∼ Bernoulli(PD)

• Loss Given Default = 1 – Recovery Rate (%)

• Expected Loss ⇐ ΕΕΕΕ[EAD x D x LGD] = EAD x PD x LGD

• Unexpected LossBasel II ⇐ EAD x PDdownturn x LGDdownturn – EL

• Value-at-Riskcredit ⇐ θ s.t. Pr(L > θ) = α∈ 1bp, 10 bp, …

• Exceedance Losscredit ⇐ ΕΕΕΕ[L|L > θ]

• Credit Derivatives, e.g. Credit Default Swaps (CDS), Credit

Linked Notes (CLN), Collateralized Debt Obligations (CDO)

Modelling Credit Obligor Risk

• Credit as a Commercial Banking Business• Business Line:

• Wholesale vs. Commercial vs. Retail

• Business Acquisition:

• Term Lending vs. Trade Finance/Contingent* vs. Credit Lines vs.

• Business Process:

• Origination vs. Maintenance** vs. Rehabilitation

• Business Control:

• Business Unit vs. Risk Management vs. Compliance Function

• Business Performance:

• Market Position vs. Risk-Adjusted Returns vs. Economic Capital

*not strictly contingent-claim products, i.e. credit derivatives

**excludes Investment Banking’s ‘Originate-to-Distribute’ model


• Obligor Default as an Object of Analysis• Default Event:

• Application Loan Contract (Priced, Collateralised) Drawdown Default Post-Default Pathway

Cured, Restructured, Sale/Liquidation

• Default Arrival:

• ‘Attribute’ vs. ‘Accounting’ vs. ‘Actuarial’

• Default Mapping:

• ‘Boolean’ vs. ‘Probability’ vs. ‘Time’

• Default Factor:

• ‘Demographic’ vs. ‘Behavioural’ vs. ‘Economic’


• Wholesale/Retail Obligor Discriminant Analysis• Data: (‘D’,‘B’,‘E’) → 0,1, where 1 signifies obligor default

• ‘Business Unit’ Problem:

• Inference: ‘D’ × ‘B’ × ‘E’ → ‘Approved’, ‘Rejected’, ‘Conditionally Approved’

• ‘Risk Management’ Problem:

• Inference: ‘D’ × ‘B’ × ‘E’ → Pr(D = 1) ≤ Threshold Limit?

• ‘Commercial Banking’ Problem:

• Inference: ‘D’ × ‘B’ × ‘E’ → ‘Approved’, ‘Rejected’, ‘Conditionally Approved’,

s.t. Pr(D = 1) ≤ Threshold Limit, ↑↑↑↑ Bank’s Return on Economic Capital

Risk Management vs. Business Process

Identify(10%)

Measure(60%)

Mitigate(20%)

Report(10%)

Decide(10%)

Monitor(20%)

Market(10%)

Analyse(60%)

Upstream vs. Downstream Risk Analytics

Business

ModelRisk

Strategy

Credit

Decision

<< upstream analytics

downstream analytics >>

RiskMeasure.

CapitalAdequacy

RegulatoryCompliance


• Wholesale/Retail Credit Risk Analytics• Data: (‘D’,‘B’,‘E’) → 0,1, where 1 signifies obligor default

• ‘Business Unit’ Analytics:

• Linear Factor Scorecard, with Cut-Off & Override Protocols

• ‘Risk Management’ Analytics:

• Logistic Regression Analysis, etc. ⇒ PD/LGD/EAD Estimation

• ‘Commercial Banking’ Analytics:

• Basel II: PD × LGD × EAD → Economic Capital Cost


• Issues

• Linear vs. Nonlinear Factor

• Can be addressed by way of ‘pre-processing’, i.e. by ‘bucketing’ ⇒ ordinal input variables

• Linearly vs. Nonlinearly Separable Space

• Must resort to higher class of function, i.e. Artificial Neural Network (ANN)

• In-Sample vs. Out-Sample Performance

• Requires rigorous Model Validation Programme

14

Data

Model

Parameter

Analytics

Risk Analytics vs. Model Validation


• Wholesale Credit Rating Transition Matrix

• (Finite) Discrete Number of States

• ‘Memoryless’ State Transition Probability

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• Continuous-Time Markov Process

• Matrix of State Transition Intensities

• Can work out State Transition Probability Matrix as well

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• ‘Risk-Neutral Pricing’ of Defaultable Bonds

• Reminder: forward price ≠ future spot price

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Modelling Credit Portfolio Risk

• Conundrum• If X ∼ Ν(µX,σX

2) & Y ∼ Ν(µY,σY2)

can be jointly Normal, i.e. X ∼ Ν(µµµµ,Σ)

• How come X ∼ Bernoulli(ρX) & Y ∼ Bernoulli(ρY)

cannot be jointly Bernoulli?

• Quick Fix

• Bernoulli Mixture: let PX and PY be jointly distributed, then once randomness resolved, i.e. PX = pX & PY = pY,

simply use X ∼ Bernoulli(pX) & Y ∼ Bernoulli(pY)


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• Issues

• Are Defaults Independent?

• No, so now what?

• Are Risks Additive?

• No, so now what?

• What went wrong w/ Collateralized Debt Obligations (CDO)vis-à-vis the US Subprime Mortgage Crisis?

• Plenty, so now what?

Copula โคปลา นาจะเปนคาตอบ!

• What’s wrong w/ plain ‘correlation’?

• Doesn’t work with Non-Normal Random Variables

• What is & what’s wrong w/ ‘Gaussian Copula’?

• Like plain ‘correlation’ only works with non-normal r.v.

• But cannot capture:

• Asymmetric Dependency Structure

• Nonlinear Dependency Structure

• Extreme Dependency Structure

• Dubbed (in a rather ‘unkind’ 2009 Wired Magazine article):

• “The Formula That Killed Wall Street”[http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all]

Copula โคปลา นาจะเปนคาตอบ!

• What is this thing ‘copula’?

• Just think ‘generalised correlation’

• Allows you to model dependency realistically and separately from how you model individual random variables (i.e. risks).

• And because there are many, many types of copulas out there, you can pick one that captures, say, why stocks seem to ‘correlate’ less in an ‘up’ market than in a ‘down’ one, or more on ‘highly volatile’ days than on ‘calm’ days.

Gaussian Slug CopulaConstructing a Gaussian Slug copula requires modification only w.r.t. the bivariate integrand:

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Figure 1: Standard Gaussian vs. ‘Gaussian Slug’ Copula Density – 3D Plots

Figure 2: Standard Gaussian vs. ‘Gaussian Slug’ Copula Density – Contour Plots

Nacaskul, P. & Sabborriboon, W.(2009) “Gaussian Slug – Simple Nonlinearity Enhancement to the 1-Factor and Gaussian Copula Models in Finance, with Parametric Estimation and Goodness-of-Fit Tests on US and Thai Equity Data”, 22nd Australasian Finance and Banking Conference, 16th-18th December, Sydney, Australia, [http://papers.ssrn.com/abstract=1460576].

Quantitative Models & Enterprise Analytics

[15 May 2013]

• Semi-Structured Data, “the Internet of Things”

• Banking Service Delivery, Enterprise Risk Analytics…

• Stochastic Models, Optimisation, Simulation…

• ‘Quants’ (math. sound, prototyping skills)

People Technology

DataOpportunity

Poomjai Nacaskul – Publication

2012 (w/ Janjaroen, K. & Suwanik, S.) “Economic Rationales for Central Banking: Historical Evolution, Policy Space, Institutional Integrity, and Paradigm Challenges”, Bank of Thailand Annual Symposium, 24th September, Bangkok, Thailand, [http://papers.ssrn.com/abstract=2156808] [http://www.bot.or.th/Thai/EconomicConditions/Semina/symposium/2555/Paper_1_EconRationalesCentralBanking.pdf] (w/ Thai abstract) & [mms://broadcast.bot.or.th/magstream/20120924_01.wmv] (video).

2012 “Systemic Importance Analysis (SIA) – Application of Entropic Eigenvector Centrality (EEC) Criterion for a Priori Ranking of Financial Institutions in Terms of Regulatory-Supervisory Concern”, Bank for International Settlements (BIS) Asian Research Financial Stability Network Workshop, 29th March, Bank Negara Malaysia, Kuala Lumpur, Malaysia, [http://papers.ssrn.com/abstract=1618693].

2011 “Relative Numeraire Risk and Sovereign Portfolio Management”, chapter 7 in Park, Donghyun(ed., 2011), Sovereign Asset Management for a Post-Crisis World, pp. 71-84, London: Central Banking Publications, [ISBN: 978-1-902182-71-1] [http://papers.ssrn.com/abstract=2156855] [http://riskbooks.com/sovereign-asset-management].

2010 “Toward a Framework for Macroprudential Regulation and Supervision of Systemically Important Financial Institutions (SIFI)”, SSRN Working Paper Series, [http://papers.ssrn.com/abstract=1730068].

2010 “Financial Modelling with Copula Functions”, Lecture Notes, [http://papers.ssrn.com/abstract=1726313].

2010 “The Global Financial (nee US Subprime Mortgage) Crisis –12 Contemplations from 3 Perspectives”, SSRN Working Paper Series, [http://papers.ssrn.com/abstract=1677890].


2009 (w/ Sabborriboon, W.) “Gaussian Slug – Simple Nonlinearity Enhancement to the 1-Factor and Gaussian Copula Models in Finance, with Parametric Estimation and Goodness-of-Fit Tests on US and Thai Equity Data”, 22nd Australasian Finance and Banking Conference, 16th-18th December, Sydney, Australia, [http://papers.ssrn.com/abstract=1460576].

2009 “International Reserves Management and Currency Allocation: A New Optimisation Framework based on a Measure of Relative Numeraire Risk (RNR)”, Joint BIS/ECB/World Bank Public Investors Conference, 16th-17th November, Washington, DC, USA, [http://papers.ssrn.com/abstract=1618692].

2006 “Adopting Basel II – Policy Responses in Case of Thailand”, chapter 12, pp. 80-97, in Kim, H.-K. & Shin, H. S. eds., Adopting the New Basel Accord: Impact and Policy Responses of Asia-Pacific Developing Countries, Proceedings of the Korea Development Institute (KDI) 2006 Conference, 6th-7th July, Seoul, Korea.

2006 “Survey of Credit Risk Models in Relation to Capital Adequacy Framework for Financial Institutions”, [http://papers.ssrn.com/abstract=1625254].


1999 (w/ Dunis, et al.) “Optimising Intraday Trading Models with Genetic Algorithms”, Neural Network World, v. 5, pp. 193-223.

1998 (w/ Dunis, et al.) “An Application of Genetic Algorithms to High Frequency Trading Models: a Case Study”, chapter 12, pp. 247-278, in Dunis, C. & Zhou, B. eds., Nonlinear Modelling of High Frequency Financial Time Series, [John Wiley & Sons, Chichester, UK].

1997 “Phenotype-Object Programming & Phenotype-Array Datatype: an Evolutionary Combinatorial-Parametric FX Trading Model”, Proceedings of the 1997 International Conference on Neural Information Processing (ICONIP’97), Dunedin, New Zealand, [Singapore: Springer-Verlag].

(version) Forecasting Financial Market (FFM) ’97, London, UK.

(version) Emerging Technologies Workshop ’97, University College London.

1996 “A Neuro-Evolutionary Framework for Fuzzy Soft-Constraint Optimisation: An FX/Futures Trading Portfolio Application”, Proceedings of the 1996 International Conference on Neural Information Processing (ICONIP’96), Hong Kong, [Singapore: Springer-Verlag].

(version) Forecasting Financial Market (FFM) ’96, London, UK.

(version) 1996 International Symposium on Forecasting (ISF), Istanbul, Turkey.

nacaskul, poomjai (2006), “survey of credit risk …€¢ credit derivatives, e.g. credit default...

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