Jameel ’ s Dimensional Stressed Default Probability Models are Indeed IFRS 9 Complaint Models

Default Probabilities can be used to Analysis Firm Creditworthiness, calculate Expected Credit Losses, Economic and Regulatory Capitals for Banking Institutions and Ranking such as FICO for consumers or Bond Ratings from S & P, Fitch or Moodys for Corporations and Governments. Banks and other Institutions are heavily investing towards Building, Developing, Improving and or Purchasing Credit Risk Models that would enhance their capabilities to handle, predict and quantify Credit Risk challenges which will subsequently help them to accurately calculate and assign sufficient Economic and Regulatory Capitals. It is believe that the existing Default Probability Models failed to accurately predict the unforeseen level of borrower defaults and resulting losses they had to recognize. The IASB in July, 2014 issued the final version of IFRS 9 Measurement of Financial Instruments beginning on or after 1st January, 2018 with early adoption permitted. It replaces IAS 39 Financial Instruments: Recognition and Measurement. IFRS 9 require adjustments to the use of Probability of Default (PD), Exposure at Default and Loss Given Default (LGD) estimates. Probability of Default (PD) plays very important role when Calculating Expected Credit Losses under IFRS 9. Jamilu (2015) enhanced LOGIT and PROBIT Default Probability Models with the aid of one-dimensional forward-looking information ( ) satisfies Jameel’s Criterion and positive average of economic forecasts of future macroeconomic scenarios μ > 0, ≥ 1 . This paper further enhance LOGIT and PROBIT Default Probability Models using Two and Three Dimensional Forward-Looking Information(s) ( ), ( ) and ( ), ( ), ( ) respectively satisfies Jameel’s Criterion with LOG-LOGISTIC (3P) ≡ ( ) , CAUCHY ≡ ( ) and BURR(4P) ≡ ( ) and positive average of economic forecasts of future macroeconomic scenarios μ . The paper tested the performances of only proposed Default Probability Models of TYPES 1 in each class using Twenty One (21) working days (from 12/1/ 2014 to 12/30/ 2014). The results were fascinatingly interesting, impressive, viable, reliable, sophisticated, and complaint with IFRS 9 since they incorporated forwardlooking information(s) and Economic forecasts of the future macroeconomic scenarios thereby minimizing the differences between MODELS DEFAULT PROBABILITIES and REAL LIFE DEFAULT PROBABILITIES.


Introduction
In July, 2014 IASB issued the final version of IFRS 9 Measurement of Financial Instruments beginning on or after 1 st January, 2018 with early adoption permitted.It replaces IAS 39 Financial Instruments: Recognition and Measurement.The major target of accounting standards is to provide financial information that stake-holders would find useful when making decisions.The most challenging aspects required by IFRS 9 are the treatment on incorporation of forward-looking information and economic forecasts of future macroeconomic scenarios into the existing Default Probability Models.The IFRS 9 accounting rules regarding Measurement of Financial Instruments will NORROW the wide gaps between Models Default Probabilitiesand Real Life Default Probabilities.
(2016) argued that Regulatory Stress Testing requires that the models should demonstrate sensitivity to macroeconomic conditions.
In response to the credit crisis of 2007-2008, the banking sector adopted international financial regulations to lessen their exposure to default risk.The Basel Committee on Banking Supervision's (BCBS) Goal is to improve the existing banking sector's strategies, processes and ability to deal with FINANCIAL STRESS effectively.Under IFRS 9 Credit Risk Modelling, IFRS 9 reason was that "… the Credit Risk at Origination is included in the Pricing of Financial Asset but any increase in Credit Risk is NOT".
It is believe that the existing Default Probability Models failed to accurately predict the unforeseen level of borrower defaults and resulting losses they had to recognize.Financial Institutions are devoting serious amount of time, energy and resources towards building, developing and purchasing CREDIT RISK MODELS that may improve their abilities to predict and quantify CREDIT RISKS they faces.These credit risk models can adequately improve their abilities to sufficiently calculate Economic and Regulatory Capital reserves.These efforts have been recognized and promoted by Bank Regulators and their Macro prudential Policies.
To address Bankers and Regulators late complain that "If only we had seen this coming or had been better prepared…" Jamilu (2015)   The modelling approach for the key risk parameters will be affected by the incorporation of forward -looking, credible and robust economic scenarios into ACCOUNTING MODELS.Banks faces number of challenges in meeting their designed level of IFRS 9 requirements for instance SOPHASTICATED MODELLING EXPECTATIONS, CORRECT MODELS, PEOPLES and SKILLS.

Materials
Geometric Volatility σ and Geometric Return μ of the Arithmetic Means of the underlying Asset Return plus Returns of the explained (independent) variables as well as Jameel's Criterion based Best fitted fat-tailed Probability Distribution of the underlying Asset Return , μ , , as worked out below: • SHRINKING the NORMAL Probability of Default ( ) to CONTRACTIONAL Probability of Default ( ) using economic forecasts of future macroeconomic scenarios of Geometric Volatility σ ≥ 1 and Only positive Geometric Return μ > 0, infinitesimal of the Arithmetic Means of the underlying Asset Return plus Returns of the future macroeconomicparameters as well as Jameel's Criterion Best fitted fat-tailed forward-looking information ( ), ( ) for Two Dimensional and ( ), ( ), ( ) for Three Dimensional of the underlying Asset Return, where ( ), ( ) ( ) are 1 st , 2 nd and 3 rd Distributions Ranking according to Jameel's Criterion.
• BLOWING the NORMAL Probability of Default ( ) to EXPANSIONAL Probability of Default ( ) using economic forecasts of future macroeconomic scenarios of Geometric Volatility σ ≥ 1 and Only positive Geometric Return μ > 0, infinitesimal of the Arithmetic Means of the underlying Asset Return plus Returns of the future macroeconomic parameters as well as Jameel's Criterion Best fitted fat-tailed forward-looking information ( ), ( ) for Two Dimensional and ( ), ( ), ( ) for Three Dimensional of the underlying Asset Return, where ( ), ( ) ( ) are 1 st , 2 nd and 3 rd Distributions Ranking according to Jameel's Criterion.

Logit Default Probability Model
PD is the probability of default. is a vector of explanatory variables (Macro-economic Indicators).

Propose Three-Dimensional Stressed Logit Default Probability Models
TYPE 1:

Propose Two-Dimensional Stressed Probit Default Probability Models
TYPE 1: 2.5.6 Propose Three-Dimensional Stressed Probit Default Probability Models TYPE 1: is Optimal reference to LOGIT and CONVERGE TO REAL LIFE DEFAULT PROBABILITIES for each 1,2, … , .
(ii) = ( )is Optimal reference to PROBIT and CONVERGE TO REAL LIFE DEFAULT PROBABILITIES for each 1,2, … , .
(iii) Or the difference between the MODEL DEFAULTPROBABILITIES and REAL LIFEDEFAULT PROBABILITIES will be very NEGLIGIBLE or even possibly ZERO at many points in time .Note that one can work out for the other proposed model TYPES.

Empirical Results
Assume, the data distribution Mean equal 0, Standard

Discussions
In this paper, the performances of the PROPOSED MODELS with respect to LOG-LOGISTIC (3P), CAUCHY, and BURR (4P) can be improved using the following: (1) Accurate prediction of economic forecasts of fundamental macroeconomic parameters used in the proposed models (2) The Author set the Log-Logistic (3P) parameter to be 1 and Burr (4P) parameters = 1, = 1, = 1, = 1 = 2 thus collapsed to almost Normal.With HIGH VALUES of , , , , , and , the proposed Jameel's Stressed Closed Prices will effectively approximates the REAL PRICES.
(3) Jameel's Criterion axiom known as "Criterion Enhancement Axiom" : That if we could be able to Runs the Goodness of Fit Tests such as the RANKS of Kolmogorov Smirnov (KS) used Jameel's Contractional-Expansional Stressed Methods and Jameel's Criterion to CAME UP with Advanced Stressed Models capable of capturing IFRS 9 INCREASE IN CREDIT RISK that is NOT included at the origination in the PRICING of Financial Assets, Derivatives and Expected Credit Losses (ECLs) components (PD, EAD, LGD) as argued under IFRS 9 Credit Risk Modelling.The objectives of this paper is to further enhance LOGIT and PROBIT Default Probability Models using Two and Three Dimensional Forward-Looking Information(s) ( ), ( ) and ( ), ( ), ( ) respectively satisfies Jameel's Criterion with LOG-LOGISTIC (3P) ≡ ( ) , CAUCHY ≡ ( ) and BURR(4P) ≡ ( ) and positive average of economic forecasts of future macroeconomic scenarios μ > 0, ≥ 1 .
adjustments to the use of Probability of Default (PD), Exposure at Default and Loss Given Default (LGD) estimates.As from the above figure, Probability of Default (PD) plays very important role when Calculating Expected Credit Losses under IFRS 9.

PREDICTED PRICE PATH will finitely coincides many times with the REAL PRICE PATH of the stock under consideration. 2.2 Methods Figure
Published by IDEAS SPREAD 2.1.2Probability of Default (Pd) or Default ProbabilityThis can be defined as a term describing the likelihood of a Default over a particular time horizon.It provides an estimate of the likelihood that a borrower will be unable to meet its debt obligations.PD is used in a different Credit Analyses and Risk Management Frameworks.
1. Jameel'sContractional-Expansional Stressed Methods From figure 1, the basic Idea was to initially use Jameel's Contractional-Expansional Stress Methods to incorporate Low-Probability, High-Impact into the Default Probability Models: LOGIT and PROBIT Models using

Table 2 .
Propose Three-Dimensional Stressed Logit Default Probability Models TYPE 1

Table 3 .
Propose Two-Dimensional Stressed Probit Default Probability Models TYPE 1

Table 4 .
Propose Three-Dimensional Stressed Probit Default Probability Models TYPE 1

Areas in Table 1 to 4
shows NORMAL DEFAULT PROBABILITIES while the Un-shaded Areasshown the performances of the proposed Dimensional Default Probability Models vis-à-vis NORMAL DEFAULT PROBABILITIES.However, the scope of the research work is to compare the proposed Dimensional Default Probability Models with the Normal Default Probabilities as the Real LifeDefault Probabilities are NOT at the Author's disposal.
The results performances were FASCINATINGLY interesting, impressive, viable, reliable, sophisticated and complaint with IFRS 9 since they incorporated the forward-looking information satisfiesJameel's Criterion and Geometric average of only positive Economic forecasts of the future Macroeconomic scenarios μ > 0, ( ≥ ) and also minimized the differences betweenModel Default Probabilities and REAL LIFE DEFAULT PROBABILITIES.
Test, Anderson-Darling Test, Jarque and Bera (JB) Test, Shapiro Wilk (SW) Test, Cramer-Von Mises Test, Pearson Test, Lilliefors Corrected K-S Test, D'AgostinoSkewness Test, Anscombe-Glynn Kurtosis Test, D'Agostino-Pearson Omnibus are all UNITY (1) of the underlying Stock Returns then the proposed Jameel's Stressed Closed Prices will coincide at finitely many points with the REAL PRICES .(4) μ can be TESTED as ARITHMETIC Means of only positive Arithmetic Means of the Underlying Asset Return and Returns of the future economic forecasts of macroeconomic parameters, otherwise should remainsGEOMETRIC MEANS as defined and used in the paper.LOGIT and PROBIT Models were first applied to Financial Markets byOhlson (1980) and Zmijewski (1984) to predict bankruptcy and to estimate probability of default respectively.Logit possesses FATTER TAILS than Probit and that makes it more robust to calculate Default probabilities.However, with the advancement in Information and Telecommunication Technology, Natural Disasters, Civil Unrest, Terrorism, Stock Market Crashes and Bubbles, Banks and other Institutions find it very difficult to accurately calculate Default Probabilities of their Borrowers, thus, Logit, Probit and other Default Probability Models needs to be enhanced to be abled accurately Quantify and Predict potential Credit Risk face by those Institutions.Jamilu (2015) enhanced LOGIT and PROBIT Default Probability Models with the aid of one-dimensional forward-looking information ( ) satisfies Jameel's Criterion and positive average of economic forecasts of ( )