CDS Rate Construction Methods by Machine Learning Techniques - PDF document

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/317273929 CDS Rate Construction Methods by Machine Learning Techniques (Presentation Slides) Article in SSRN Electronic Journal · January 2017 DOI: 10.2139/ssrn.2973065 CITATIONS READS 0 468 1 author: Zhongmin Luo Birkbeck, University of London 18 PUBLICATIONS 16 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Machine Learning and Application in Finance View project No-arbitrage conditions for CDS-term-structure, Aribitrage opportunities and Implications View project All content following this page was uploaded by Zhongmin Luo on 27 November 2018. The user has requested enhancement of the downloaded file.

CDS Rate Construction by Machine Learning Techniques Zhongmin Luo 07-March-2017 * Department of Economics, Mathematics and Statistics, Birkbeck, University of London and Standard Chartered Bank, London, UK jointly Raymond Brummelhuis Uni niversity of of Re Reims Champagne-Ardenne Department of Mathematics and Computer Science Reims, France And Department of Economics, Mathematics and Statistics, Birkbeck, University of London, UK Raymond and Luo, Zhongmin, CDS Rate Construction Methods by Machine Learning Techniques (May 12, 2017). Available at SSRN: https://ssrn.com/abstract=2967184 * A presentation delivered at the invitation by London School of Economics. Disclaimer; thanks for feedbacks from participants and the views and opinions expressed in the presentation are those of the authors and do not necessarily reflect the practices or positions of above affiliated institutions.

Agenda 1. Set the scene and contexts 2. The Machine Learning Technique based Solution 1) A very brief summary of Machine Learning Technique based CDS Proxy Methods 2) A very brief summary of three top classification performers: Neural Network (NN), Support Vector Machine (SVM) and Ensemble/Bagged Tree. 3) A very brief summary of Cross-classifier Performances including other five classifier families: Discriminant Analysis (DA), Naïve Bayes (NB), 𝑙 Nearest Neighbours ( 𝑙 NN), Logistic Regression (LR) and Decision Tree (DT) 4) Parameterization choices for classifiers; regularization; optimal parameterizations and tuning 5) Correlation impacts on classification performances. 3. Conclusions 4. Q&A 2

The Scene: what would be our lo losses if if X or Y default? • Lehman declared bankruptcy on 15Sep08; on the side of leafy Green Park in London at one of largest European hedge funds, two questions pop up: • What would be our losses to Bank X (which has liquid CDS quotes) if it defaults within the coming year? It’s a fair question after seeing what happened to Lehman. • What would be our losses to a Pension Fund Y (which doesn’t have liquid CDS quotes) if it defaults within the coming year? It’s a tricky question! • To answer the second question above, financial institutions employ so-called CDS proxy method ; CDS proxies are extensively used in XVA pricing, credit risk management. 3

1.1 .1 A Shortage of f Liq iquidity Pro roblem • In response to the financial crisis in 2008, Banking regulator and Accounting Standard Board have required F inancial I nstitutions to measure Counterparty Default Risks and make CVA/FVA (XVA) Adjustment based on Credit Default Swap (CDS) for their counterparties, either observed or proxied based on so-called CDS Proxy Method . • Shortage of Liquidity problem : in reality, the vast majority of FIs’ counterparties don’t have liquid CDS quotes. An European Bank Counterparty Distribution by Regions/Sectors ( Overall: 84.4%; EBA Survey: >75%) % of Counterparties in Regions/Sectors 99% 96% 95% 94% 100% 91% 90% 89% 87% 84% 83% 90% 82% 80% 70% 70% 63% 60% 50% 40% 30% 20% 10% 0% 4 Observables Nonobservables

S Pro roxy Methods 1.2 .2. . Regulatory ry Cri riteria and Two Exis xisting CDS Regulatory Criteria 1. The CDS Proxy Method has to be based on an algorithm that discriminates at least 3 types of variables: Region, Industry and Credit Quality (e.g., rating). 2. Both the observable counterparty (or observables) and the nonobservable counterparty (or nonobservables) come from the same peer group defined by the above three variables. 3. The appropriateness of a Proxy CDS Spread should be determined by its CDS spread volatility across the constituents within the bucket and not by its level; i.e., any CDS Proxy Method should reflect the idiosyncratic components of counterparty default risks. Two Existing CDS Proxy Methods 1. Credit Curve Mapping : proxies CDS rates by the mean/median of CDS rates within a Region/Sector/Rating bucket. Cross-sectional Regression : explains a term-specific CDS rate for counterparty 𝑗 2. (denoted by 𝑇 𝑗 ) by its response ( 𝛾 ) to the event whether the counterparty belongs to a region ( 𝑆 ), sector ( 𝑇 ), rating ( 𝑠 ) or seniority ( s ), indicated by respective indicator function 𝐽 , estimated by running a Cross-sectional regression for each CDS term as shown below: 5

1.3. Research Gaps and Research Objectives Research Gaps 1. As CDS Curve Proxy Method • Credit Curve Mapping : the bucket-specific CDS means/medians only represent bucket-average default risk level; neither does it represent counterparty-specific default risk nor does it represent the volatility of default risks across the counterparties within the bucket. • Cross-sectional Regression : for each CDS term, one regression is run for the bucket; like Curve Mapping Method, it fails to account for counterparty-specific default risk and volatility within the bucket. Furthermore, it potentially can introduce Arbitrage Opportunities by producing ‘’inverted CDS curve’’ for the bucket even in cases where many counterparties within the bucket have ‘’normal’’ upward -sloping curves. • Bond spreads include significant liquidity premiums as indicated by literature, thus, are not good choice for CDS Proxy. 2. As Classifier Performance Comparison based on financial market data : Given the large number of potential classifier candidates, the question of cross-classifier performance comparison arises; existing Classifier Performance Comparison studies [7][8] are based on non-financial market data. Research Objectives 1. A research for CDS Proxy Methods based on Machine Learning Techniques. 2. Classifier Performance Comparison based on financial market data in the search for a best-of-best solution to the problem discussed on Slide #4. 6

1.4 .4. . Mean and Std. of 5-year CDS for Europe/Banking/A-rated counterparties • On 15Sep08, Lehman Brothers EU (declared Bankrupt), CommmerzBank, Credit Suisse, Standard Chartered, Macquarie EU, Wachovia, UniCredit, Fortis (Nationalized by Dutch government), AIB (Nationalized by Irish government), North Rock (Nationalized by UK government) are all rated ‘A’, should they all be treated equal for counterparty default risk based on the fact that they belong to the Europe/Banking/A-rating bucket ? • On 15Sep08, it’s obviously wrong to use one bucket-level CDS proxy spread (Average-A 370 bps in Blue below) to represent the default risks of all counterparties, which have significant amount of idiosyncrasies as shown by the day’s CDS volatility of 620 bps (std-A in Red below) within the above Europe/Banking/A-rating bucket. 7

2.1 .1 A Machine Learning Technique based Solu lution Given a so-called Training Set 𝐸 𝑈 with 𝑧 𝑗 for class label and 𝑦 𝑗 for Feature Vector, as shown below: Machine Learning Techniques enable us to construct a mapping called 𝐺 𝜄 (𝑦) shown below; 𝜄 is learned from 𝐸 𝑈 based on a given algorithm or a Classifier Family available from Machine Learning. An algorithm from a Classifier Family with a specific parameterization choice is referred to as a Classifier . In this paper, we studied 8 Classifier Families and presented 156 Classifiers out of hundreds of different parameterization choices based on “top - 3” principle. 8

2.2. Feature Sele lections: based on empirical experience and lit literature 9

2.3 .3 Eig ight Cla lassifier Families and 156 Cla lassifiers 1. Neural Network (NN): e.g., Activation Functions, # of hidden units 2. Support Vector Machine (SVM): e.g., kernel functions 3. Ensemble Bagged Tree (BT): e.g., the number of learning cycles. 4. Discriminant Analysis (DA): e.g., Linear/Quadratic; regularization. 5. Naïve Bayes (NB): e.g., Kernel choices; bandwidth selections. 𝑙 Nearest Neighbours ( 𝑙 NN): e.g., Distance metrics; 𝑙 in 𝑙 NN. 6. 7. Logistic Regression (LR). 8. Decision Tree (DT): e.g., Impurity measure choices; Tree sizes. 10

2.4 Eig ight Classifier Families and 156 Classifiers 11

2.5 Cro ross/Intra-classifi fier Performance for Our CDS Pro roxy Methods 12

imple 𝒐 Unit 2-layer Neural Network 2.6 A Sim Activation Functions Output transform with n Hidden Units: functions: Softmax e.g., Sigmoid function function FS/d is # of features Fitting of Neural Network 13

2.7 Mathematical Representation of f Neural Network Top preforming Minimizing the Cross-Entropy Activation Functions 14

2.8 Neural Network performance for r CDS Pro roxy Method 15

2.9 Support Vector Machine for Li Linearly Separable Data Maximizing the margin in case of linearly separable data 16