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  • 1. Indizen Quantitative Solutions Corporate Presentation Contact details: paco.sanchez@indizen.com ℡ + 34 615 903 579 1
  • 2. 2 Indizen Technologies Indizen is a company that specializes in technology and quantitative analysis. We provide these services to our clients in three different ways: We provide our clients with timely access to cost effective, indizen highly qualified professionals with advanced technological human capital and quantitative skills. We deliver closed projects for our clients. By using our own indizen development methodology and architecture iMade we labs guarantee a prompt and robust delivery. indizen We offer quantitative models and solutions to help our clients quantitative make the best business decisions. We have a sound, proven solutions experience in the modeling of financial markets and operations.
  • 3. 3 Corporate Principles • Our employees are our most valuable asset. Their knowledge, experience and ingenuity are the key factors for the success of our projects. • We actively encourage our employees to share their ideas, creativity and skills so that they became part of the global knowledge of the company. • We promote innovation and creativity in our work. • Our relationship with our clients is based in the highest ethical standards of honesty. • We develop our work with the highest levels of scientific objectivity in order to provide tools to make the best business decisions. • We are committed to using the most appropriate techniques and technologies for the benefit of our clients.
  • 4. 4 Who we are Enrique Mota is the CEO of Indizen Technologies and since the foundation of the company he is responsible for business development. He has actively participated in some of our most relevant R&D&i projects in the health industry, telecom, finance and energy and he deployed our proprietary methodology for project development (iMade), which is a key factor for a successful delivery of our projects by monitoring the quality of the innovation process. He is currently focusing on the analysis of the natural language and the ways to apply semantic models in order organize and classify information according to different coding international standards. These techniques are applied in different commercial software packages that we offer to the health care sector. Quique holds a degree in Telecom Engineering from the University of Alcalá de Henares (Spain)
  • 5. 5 Who we are Daniel Crespo is one of the founding partners of Indizen Technologies. He pioneered the first steps of the company in the world of the web technologies and e-business. He has worked in several successful projects in the financial risks industry and back in 2003 he launched our first project on nuclear risks with the involvement of the Spanish Nuclear Security Council. Since 2005, Daniel is CEO of Indizen Optical Technologies a spin-off of Indizen and a joint venture with a number of university professors created to develop optical technologies for different industrial applications. IOT is currently active in four continents commercializing state-of- the-art software for ophthalmic lens design, with a rapidly growing portfolio of clients. Other projects involve development of optical metrology applications for Airbus and INTA (the Spanish Space Agency). Daniel holds a Ph.D. in Physics from the Universidad Complutense of Madrid.
  • 6. 6 Who we are Jesús Gil is an experienced consultant in IT. Previous to the creation of Indizen Technologies, in which he is one of the founding partners, he worked as an IT consultant for large consulting firms as well as for the public administration. In these activities he acquired extensive experience in the modeling, design and development of large systems, and in the management of large teams of consultants. He leads complex simulation projects, such as one of particular interest for the Company related to safety and risks control in nuclear power plants, currently in use by the Spanish Nuclear Security Council. Since 2007 Jesús is CEO of Szena Risk, a joint venture with Indizen and a group of financial consulting experts, aimed at developing software solutions for the Financial Industry with focus on Risks Management and Pricing Models. Szena has a portfolio of technological solutions with a presence in major Spanish financial institutions. He has a degree in Theoretical Physics from the Universidad Autónoma de Madrid.
  • 7. 7 Who we are Alberto Gómez joined Indizen Technologies in 2002. He is currently the CTO of the firm and manages the Distributed Systems areas of the company and Financial Projects. He successfully managed several complex projects for the main clients of the company in the development of the market risk management system, the counterparty credit exposure calculation system at Santander and the external models valuation system at Caja Madrid. Before joining Indizen he lead IT projects in different fields such as Terrestrial Digital TV, Telecommunications and CAD/CAM in engineering and R+D departments. He has a wide experience in financial risks and grid technologies and is an expert in software development methodologies and programming languages. He has a master degree in Telecommunication Engineering from the Universidad Politécnica de Madrid, an Executive Master in Financial Risk management and is certified Financial Risk Manager (FRM) by the Global Association of Risk Professionals (GARP).
  • 8. 8 Who we are Paco Sanchez is the most recent partner at Indizen Technologies. He has joined the company to develop and expand the consulting branch Indizen Quantitative Solutions with a particular focus in providing quantitative consulting services to Large Corporations and Financial Institutions. Until June 2009 Paco pursued a successful fourteen- year career at Santander, where he became Global Head of Risk Methodologies after having attained other managerial and quantitative roles. As the global head of risk methodology, he was responsible for all of the risk modeling factory, from steering the design of quantitative tools used for credit and market risk management to leading the definition of the group wide economic capital model. He supervised the development of the rating and scoring models, the development of pricing models used for model validation and all the quantitative support required from the different Risk Management Areas. He holds a Ph.D. in Physics from the Universidad Complutense de Madrid.
  • 9. 9 Indizen Quantitative Solutions indizen Quantitative models and tools quantitative solutions for the financial industry IQS is a group of highly qualified specialists in the development of IQS is a group of highly qualified specialists in the development of quantitative models for the management and control of financial quantitative models for the management and control of financial risks. risks. We develop bespoke models and applications for risk We develop bespoke models and applications for risk management, valuation, pricing, rating, operations control and management, valuation, pricing, rating, operations control and end-of-day reconciliation. end-of-day reconciliation. We have a set of software libraries for quantitative analysis and risk We have a set of software libraries for quantitative analysis and risk management that can be implemented into our clients’ systems, management that can be implemented into our clients’ systems, giving them the ability increase their quantitative power in a cost giving them the ability increase their quantitative power in a cost effective way. effective way.
  • 10. 10 Services We help organizations to improve their risk assessment and evaluation. We are specialist in risk management and portfolio analysis. Banking Banking Financial Financial Treasury Treasury book book Institutions Institutions Risk Risk Function Function Institutional Institutional Investor Investor Infrastructure Infrastructure Governance Governance Control Control & Methodology & Methodology Organization Organization Risk appetite Models Risk appetite Models Policies Planning Platforms Policies Planning Platforms Strategy Metrics && Limits Large Strategy Metrics Limits Research Research Large Compliance Compliance Risk assessment Risk assessment Corporations Corporations Action plans Action plans Areas of expertise
  • 11. 11 Services We provide quantitative consulting services, software libraries and systems to help organizations better measure and anticipate risks and make the best business decisions. Valuation Reporting Quantitative Resources Quantitative Resources Pricing Pricing and / / or and or Metrics Metrics models models Financial Library Financial Library Market and Simulation Scenario analysis Simulation Credit Risk models models Economic Capital
  • 12. 12 Services Our models provide a quick solution for market and credit risk and give an answer to problems of increasing importance such as Incremental Risk Charge and a proper computation of Potential Future Exposure, features that are fully integrated in our engines. Our professionals have also extensive experience in modeling of structural risks, scenario analysis, stress testing, credit scoring and rating models. Our modular methodology can combine market, credit and ! ! operational risk into a unique risk model. We place special care in developing a model that can be integrated ! ! into different pre-existing platforms with the advantage of it being based in an open and low cost technological infrastructure.
  • 13. 13 Services Large Corporations and Institutional Investors usually have large portfolios exposed to financial risks. Portfolio Analysis We help organizations anticipate the risks that threaten their portfolios and We help organizations anticipate the risks that threaten their portfolios and Portfolio Analysis identify ways of preventing them from arising. identify ways of preventing them from arising. Corporations that do not have large teams of quantitative resources can Corporations that do not have large teams of quantitative resources can take advantage of our services to elaborate aafull portfolio’s risk profile. take advantage of our services to elaborate full portfolio’s risk profile. Portfolio Hedging Portfolio Hedging As aaconsequence of the simulations performed, optimal hedging As consequence of the simulations performed, optimal hedging strategies are proposed so that the risk profile of your portfolio matches strategies are proposed so that the risk profile of your portfolio matches your risk appetite without spending aalot of money in quantitative analysts. your risk appetite without spending lot of money in quantitative analysts. Fair Pricing Fair Pricing We provide aafull analysis of each new deal. Our simulations allow us to We provide full analysis of each new deal. Our simulations allow us to properly compute potential future exposure which will be used by financial properly compute potential future exposure which will be used by financial institutions to charge you for credit risk. A good understanding of the risk institutions to charge you for credit risk. A good understanding of the risk profile of each new deal can help your organization better negotiate aafair profile of each new deal can help your organization better negotiate fair price for your deals, saving money for your organization. price for your deals, saving money for your organization.
  • 14. 14 Services Our risk model is a modular, scalable solution that can be easily adapted to the needs of our clients no matter how sophisticated their requirements are. Simulation Mapping Valuation Aggregation Risk Risk Risky Risky Simulated Simulated Risk Risk Drivers Drivers Objects Objects Values Values Distributions Distributions Sources of risk: Curves, FX rates, Market value Market Sources of risk: Market prices, Curves, FX rates, Vol surfaces Market value changes Risk Market prices, Vol surfaces changes Principal compo- Principal compo- nents… nents… Synthetic Indices Credit Worthiness: Credit losses due Credit Synthetic Indices Credit Worthiness: Credit losses due Macro variables Rating / Scoring to default and Risk Macro variables Rating / Scoring to default and rating migration rating migration Other … … … … Risks
  • 15. 15 Services For those firms that already have their own risk engine we also provide an aggregation methodology that allows the estimation of Economic Capital. ECONOMIC CAPITAL 25 Business and Market Risk 20 strategic risks 20 35 15 18 30 16 10 14 25 12 20 5 10 8 15 0 6 10 4 5 2 0 0 Credit Risk Reputational Risk 25 60 50 20 40 15 30 10 Operational Risk 20 35 5 10 30 0 0 25 20 15 10 5 0
  • 16. 16 Recent Experiences Market Risk Model We developed the market risk engine for aalarge international bank and aa We developed the market risk engine for large international bank and Market Risk Model number of institutional investors are currently using our models. number of institutional investors are currently using our models. Credit Risk Model We are participating in aa project for aalarge institution improving its credit We are participating in project for large institution improving its credit Credit Risk Model risk assessment by better estimating credit exposure. risk assessment by better estimating credit exposure. Economic Capital We have helped aamajor bank to develop an aggregation engine used to We have helped major bank to develop an aggregation engine used to Economic Capital aggregate risks into aaunique Economic Capital figure. aggregate risks into unique Economic Capital figure. Portfolio Analysis We have developed aaPortfolio Analysis Software Suite (PASS) in order to We have developed Portfolio Analysis Software Suite (PASS) in order to Portfolio Analysis help institutions better understand their portfolios and find the best hedging help institutions better understand their portfolios and find the best hedging strategies. strategies. Rating Models We offer an innovative rating methodology that is of special interest when We offer an innovative rating methodology that is of special interest when Rating Models applied to low default portfolios. applied to low default portfolios. Pricing Models We are currently providing several banks and institutions with pricing We are currently providing several banks and institutions with pricing Pricing Models models for treasury instruments. We are also helping them integrate the models for treasury instruments. We are also helping them integrate the pricing libraries into their own systems. pricing libraries into their own systems.
  • 17. 17 Recent Experiences Worked examples
  • 18. 18 Market Risk Model Our methodology is based on the full revaluation of the portfolios in multiple scenarios simulated either Historically or by Monte Carlo methods. We apply stochastic evolution models for market factors in order to generate future 25 Simulation scenarios. Portfolios are then 20 priced under each scenario to 15 10 get future value distributions. 5 0 The advantage of this methodology is that it can be applied both for market and credit risk, producing both VaR Valuation Aggregation and credit exposure as well as it facilitates risks aggregation.
  • 19. 19 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions Identify sources Apply a Simulate Correlated of risk Evolution Model Changes • Individual Risk Factors • Time series • Principal Components • Stocks • Volatilities • Indexes • FX rates • Correlations • … scenario • Evolution models •(Mean Reverting) Normal MDC •(Mean Reverting) LogNormal time step market driver
  • 20. 20 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions
  • 21. 21 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions
  • 22. 22 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions Market Factors are defined as any risky parameters that are required as an input of a pricing function (pricer) to compute the market price of a financial instrument. The mapping process applies all simulated changes to the market factors Base Scenario in order to generate a cube of scenarios of potential values for each of the risk factors within each time step of the simulation. scenario Mapping scenario MDC time step market driver MFC time Proxy Base step market factor Scenario market market market Simulated driver factor factor values
  • 23. 23 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions The valuation process generates a cube of potential future values for each security in the portfolio at each scenario and time step. scenario scenario MFC Valuation IVC time step market factor time step instrument value Instruments Pricers definitions
  • 24. 24 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions
  • 25. 25 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions scenario scenario Aggregation IVC time time step instrument value step portfolios portfolio value
  • 26. 26 Market Risk Model Simulation Mapping Valuation Aggregation Market Market Market Market Simulated Simulated Risk Risk Drivers Drivers Factors Factors Values Values Distributions Distributions scenario scenario scenario IVC scenario MFC MDC time time time time step market driver step market factor step instrument value step portfolio value
  • 27. 27 Credit Risk Model Based on the same foundations we simulate the evolution of the credit quality of the counterparties and estimate the value of the portfolios in each scenario. We can provide an independent Credit Risk Engine or, Simulation 25 alternatively, an integrated 20 15 Market-Credit engine. 10 5 In case an independent engine is 0 chosen, a later aggregation is possible by means of our aggregation methodology. Valuation Aggregation
  • 28. 28 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Hypothesis: The credit worthiness is an unobservable variable that can be modeled by means of a linear combination of observable variables such as economic indicators, i.e. GDP, rates, indexes… plus a specific factor depending only on each counterparty. Yi Systemic risk Specific Risk Global factor Country factor Industry factor
  • 29. 29 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions es Global Economy Japan ex US China c Ind of eti d out es Brazil India Mexico Other Asia th Wholesale Other LatAm Finance yn nde pric S le UK Germany Industrial Oil & Gas b exes France Other Europe Electricity Telecom ind Middle East Services Per country / market: •Projection of the Global Economy Local Factor over the local market GDP Retail Interest Rates Unemployment •Observed values House Prices
  • 30. 30 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Wholesale K Yi = ∑ wij Z j + 1− Ri2 ε i Global Top 10 Bank j =1 Zj Orthogonal Credit Drivers K R = ∑ wij 2 2 i j =1 Services Japan India Industrial Telecom Mexico France Other Europe China Other Asia Finance Brasil Other Latam US UK Middle East Global Economy Germany Oil & Gas Electricity
  • 31. 31 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Wholesale The credit worthiness of the counterparties is mapped into rating by means of the observed Rating Transition Matrix.   Yi = w1,i ·Z1 + w2 ,i ·Z 2 + L + wN ,i ·Z N + 1 − ∑ w2,i ·ε i  j   j  CCC AA AAA AA A BBB BB B CCC D DEF B BB BBB A AAA AAA 71.55% 19.86% 5.43% 1.90% 0.24% 0.37% 0.58% 0.07% AA 2.18% 71.06% 21.14% 4.14% 0.70% 0.29% 0.29% 0.20% A 0.18% 6.43% 69.72% 19.47% 2.54% 0.80% 0.51% 0.35% BBB 0.06% 1.10% 16.43% 64.74% 11.26% 3.84% 1.77% 0.80% BB 0.07% 0.64% 5.39% 27.86% 43.23% 14.34% 6.87% 1.60% B 0.02% 0.42% 3.12% 12.95% 16.48% 45.46% 18.55% 3.00% CCC 0.16% 0.61% 2.36% 3.75% 4.26% 8.67% 74.19% 6.00% D 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% -4 -3 -2 -1 0 1 2 3 4
  • 32. 32 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Wholesale For each rating migration an economic equivalent amount is computed. If a default occurs the loss is equal to Li = 1 − Recovery the amount that cannot be recovered If a migration occurs  t rrf + si 1  Li = 1 − ∑ + the loss is equal to the difference in  i =1  (1 + rrf + s f )i (1 + rrf + s f )t    spreads  (rrf + si )(1 + rrf + s f )t + (rrf + s f ) − (rrf + si ) = 1−     (rrf + s f )(1 + rrf + s f )t  
  • 33. 33 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Retail The state of the economy is simulated by means of the different credit drivers plus a Local Latent Factor. GDP, PPP Delinquency Rate 7,00 14,00 6,00 5,00  N  Yi = β i  wL Z L + ∑+1  wij Z j  + 1− Ri2 ε i 12,00 4,00 3,00 10,00 2,00    1,00 8,00 0,00 j=K -1,00 6,00 -2,00 1980 1985 1990 1995 2000 2005 2010 4,00 N R =w + ∑w 2,00 Unemployment 2 2 2 30,00 0,00 i L ij j = K +1 25,00 1987 1990 1993 1995 1998 2001 2004 2006 20,00 15,00 10,00  2 N   wL + ∑ wij ∑ jk wki  5,00 18,00 Inflation 0,00 1980 1985 1990 1995 2000 2005 2010 βi = R i 2     16,00 14,00 j ,k = K +1 12,00 10,00 8,00 6,00 4,00 2,00 0,00 1980 1985 1990 1995 2000 2005 2010
  • 34. 34 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Retail The state of the economy is simulated by means of the different credit drivers plus a Local Latent Factor.  N  Yi = β i  wL Z L +  ∑+1wij Z j  + 1− Ri2 ε i  Global  j=K  Economy The Local Latent Factor is the projection of the Global Economy Factor over each Country/Region Z iL = α i Z1 + 1− α i2 ε L Z iL = (sin δ i ) Z1 + (cos δ i )ε L
  • 35. 35 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions Retail Each state of the economy has an expected/plausible level of losses. For a typical granular,  N −1 ( pd ) − ρ Y  homogeneous retail Li = N  i i i  portfolio, such level of   1 − ρi2   losses is given by:
  • 36. 36 Credit Risk Model Simulation Mapping Valuation Aggregation Credit Credit Simulated Simulated Risk Risk CWI CWI Drivers Drivers Losses Losses Distributions Distributions A common set of credit drivers gives 30 us the ability to aggregate both worlds: 25 Retail Wholesale Retail 20 15 10 25 5 20 0 15 10 5 25 Wholesale 0 20 15 10 5 0 Global Economy Local Simulated Credit Latent Factors Losses Distribution Wholesale Retail Credit Drivers Credit Drivers
  • 37. 37 Credit Risk Model A Three Layers Model View View Portfolio Portfolio Counterparty Counterparty Deal Deal s tie Monte Carlo MonteliCarlo bi Methodo- Methodo- Monte Carlo sta Monte Carlo in Or Closed Form Closed Form or logy or Or Equation logy Analytical (CGF) Analytical (CGF) Equation Analytical (CGF) Analytical (CGF) Intraday, on-line Intraday, on-line Complete calculation Complete calculation Allocation at calculations for new or Allocation at calculations for new or that can incorporate counterparty level. existing deals. Uses Uses that can incorporate all the necessary counterparty level. existing deals. all the necessary hypothesis for aa Very fast and stable Its stability makes it hypothesis for Very fast and stable Its stability makes it complete calculation. calculation. appropriate for complete calculation. calculation. appropriate for RAROC calculations. RAROC calculations.
  • 38. 38 Economic Capital Institutions, in general, use different risk engines to compute the different risks. Our methodology allows the aggregation of all risks, regardless of its nature, confidence level and time horizon, into a unique losses distribution. ECONOMIC CAPITAL 25 Business and Market Risk 20 strategic risks 20 35 15 18 30 16 10 14 25 12 20 5 10 8 15 0 6 10 4 5 2 0 0 Credit Risk Reputational Risk 25 60 50 20 40 15 30 10 Operational Risk 20 35 5 10 30 0 0 25 20 15 10 5 0
  • 39. 39 Economic Capital How to combine different risk types and models into a unique model? Marginal Marginal Correlation Correlation Copula Copula Distributions Distributions 11 Characterization of Characterization of 33 Find aa set of Risk Find set of Risk 55 Obtain the loss for each Obtain the loss for each risk distributions by Drivers and estimate the type of risk: estimate type of risk: estimate risk distributions by Drivers and estimate the computing the first four combination that govern the loss via the inverse computing the first four combination that govern the loss via the inverse moments each type of risk cumulative distribution cumulative distribution moments each type of risk 2 Extend distributions 4 Simulate scenarios for 6 Sort losses properly Sort losses properly 2 Extend distributions 4 Simulate scenarios for 6 to aa common Time in order they present the to common Time the Risk Drivers and the Risk Drivers and in order they present the Horizon by applying the generate aa loss percentile correlations shown in Horizon by applying the generate loss percentile correlations shown in “constant level of risk” for each marginal loss their respective risk “constant level of risk” for each marginal loss their respective risk concept distribution engines engines concept distribution
  • 40. 40 Economic Capital Risk Adjusted Return -Expected loss +Capital Return +/- Transfer prices - Expenses -Taxes RAROC RAROC == Capital Required as a protection against unexpected losses (minus expected losses) for the defined confidence level
  • 41. 41 Economic Capital Two visions • Measures the expected profitability on capital for the RAROC Op next 12 months Pre-deal • Based on estimations of expected income Profitability of the deal. (ExpectedGrossIncome(1 − CostToIncome) − ExpectedLoss )(1 − TaxRate) Capital • It is the profitability on capital according to the RAROC Cl income and capital realized during the last 12 months Post-deal • Based on recorded income and averaged capital over Profitability of last last year. the client. (RealizedGrossIncome(1 − CostToIncome) − ExpectedLoss )(1 − TaxRate) Capital
  • 42. 42 Economic Capital • The use of these two measures allow a quick evaluation of how a new deal affects the portfolio Capital Cl * RAROC Cl + Capital Op * RAROC Op RAROC Cl(+n) ≈ Capital Cl + Capital Op • Both visions have a limited horizon of one year. • It is possible to extend our vision to a lifetime measure that estimates an average profitability during the life of the deal.
  • 43. 43 Economic Capital Lifetime RAROC Time Expected Economic Capital Interest on Net Exposure Provisions Return (years) Loss Capital Flow Capital Cash Flow 0 100.000.000 315.209 6.040.455 -6.040.455 -315.209 -6.355.664 1 100.000.000 434.070 7.089.544 -1.049.088 302.023 -434.070 1.500.000 318.865 2 100.000.000 531.092 7.796.903 -707.359 354.477 -531.092 1.500.000 616.026 3 100.000.000 610.600 8.287.775 -490.872 389.845 -610.600 1.500.000 788.372 4 100.000.000 674.832 8.621.210 -333.435 414.389 -674.832 1.500.000 906.122 5 100.000.000 725.335 8.831.802 -210.592 431.061 -725.335 1.500.000 995.134 6 100.000.000 763.432 8.942.983 -111.181 441.590 -763.432 1.500.000 1.066.977 7 100.000.000 790.377 8.972.222 -29.239 447.149 -790.377 1.500.000 1.127.533 8 100.000.000 807.395 8.933.351 38.871 448.611 -807.395 1.500.000 1.180.088 9 100.000.000 815.671 8.837.737 95.614 446.668 -815.671 1.500.000 1.226.611 10 100.000.000 0 0 8.837.737 441.887 0 1.500.000 10.779.624 IRR 15,5%
  • 44. 44 Portfolio Analysis Our risk engines give us the ability to simulate the behavior of our customer’s portfolios in order to identify the principal risk factors and allow us to check the performance of different hedging strategies. Before Before After After 35.000.000 35.000.000 30.000.000 30.000.000 25.000.000 25.000.000 20.000.000 20.000.000 15.000.000 15.000.000 10.000.000 10.000.000 5.000.000 5.000.000 0 0 1-ago-09 1-ago-10 1-ago-11 1-ago-12 1-ago-13 1-ago-14 1-ago-15 1-ago-16 1-ago-17 1-ago-18 1-ago-19 1-ago-20 1-ago-09 1-ago-10 1-ago-11 1-ago-12 1-ago-13 1-ago-14 1-ago-15 1-ago-16 1-ago-17 1-ago-18 1-ago-19 1-ago-20 Notional Instrument Rate Maturity Notional Instrument Rate Maturity 200.000.000 Payer 3,00% Jun 2019 200.000.000 Payer 3,00% Jun 2019 125.000.000 Receiver 3,84% Mar 2015 125.000.000 Receiver 3,84% Mar 2015 150.000.000 Receiver 3,30% Jun 2018 150.000.000 Receiver 3,30% Jun 2018
  • 45. 45 Portfolio Analysis Generate scenarios for the risk factors that we want to stress 4.90 4.80 We apply statistical models to give a 4.70 dynamics to the risk factors: 4.60 4.50 •Interest rates Interest rate 4.40 •FX rates 4.30 4.20 •Share prices 4.10 •Volatilities 4.00 •Correlations 3.90 •Solvency 3.80 0 1 2 3 4 5 6 • Time (years) • •
  • 46. 46 Portfolio Analysis Valuate the portfolio under each scenario 20 By pricing the portfolio under each 15 scenario in different future times we 10 Value (EUR x1000) can determine which is the worst 5 situation, which are the risk factors 0 that cause such situation and when it -5 can happen. -10 -15 As a result hedging strategies can be -20 proposed. 0 1 2 3 4 5 6 Time (years)
  • 47. 47 Portfolio Analysis Scenario generation Pricing 4.90 20 4.80 15 Valor del Swap (EUR x1000) 4.70 10 4.60 Tasa de interés 4.50 5 4.40 0 4.30 4.20 -5 4.10 -10 4.00 -15 3.90 3.80 -20 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Tiempo (años) Tiempo (años) Identification of the adverse cases AND AND Design a hedging strategy … THEN THEN … and run the portfolio again
  • 48. 48 Portfolio Analysis Our methodology allows to properly capture some effects otherwise unobserved Portfolio effect or how the adverse effects of some deals can be netted by other deals. Deal A Deal B The portfolio can behave better than any of its deals rates rates Correlation or how new deals with a counterparty can help lower its risk exposure. Optimum Pricing, when a deal mitigates the risk exposure with a customer, a better price than the market can be offered.
  • 49. 49 Portfolio Analysis We aim to answer the following questions: Which is the maximum risk scenario? And, how feasible is it? What risk mitigants can help the deal to lower its risk profile? How does a particular deal affect the rest of the portfolio? What is the profitability of a portfolio compared to its level of risk? Is there any relationship between the risk profile of the deal and the credit quality of the counterparty (wrong way exposure)? How can some legal agreements help obtain a better deal (ISDA, CSA, …)?
  • 50. 50 Rating Models In the case of low default portfolios expert judgment models are a common practice in the market place; however, the use of more objective, quantitative techniques is a requisite that allows for a transparent and efficient business model. We develop quantitative rating models for low default portfolios and SME.
  • 51. 51 Rating Models A rating model is an ordering criterion to facilitate credit decisions goods Decision point Goods Bads scoring/rating Type II error Type I error Cost of opportunity Credit Risk bads The success of a rating model depends on its ability to separate the good customers from the bad ones, thus showing a correlation between the defined ordering criterion and the occurrence of credit events.
  • 52. 52 Rating Models A rating model is built by maximizing the powerstat of an ordering criteria 10 The best possible model 10 Defaults Defaults 5 5 Total population Total population The worst of the models 10 Powerstat = B/A Defaults A B 5 Total population
  • 53. 53 Rating Models What to do when there are not enough defaults? We use the CDS market to establish an objective ordering criteria. CDS spreads are averaged over a defined time window. This ordering criteria is mapped to real world distances to default. A statistical model is developed that explains the distances to default (or pd) by means of financial statements and balance sheets ratios. This model is extended to all counterparties, including those with a CDS and those without it. CDS spreads Average CDS spreads over time 25 Merton-like model to map to DtD 20 Anchoring to PD (real world) 15 bp Statistical model via regression 10 to financial statements 5 Map PD from statistical model to 0 Time rating
  • 54. 54 Rating Models Example of implementation of a LDP rating Counterparties with a CDS CDS Spreads Financial Financial Statements Statements Risk neutral DtD dtd ∗ Statistical Real world DtD dtd = dtd ∗ + µ Statistical Model Model Probability of default ( pd = N −1 dtd ∗ + µ ) PD PD All Counterparties All Counterparties Master Scale Best agreement to aa Best agreement to reference, i.e. CAPM, reference, i.e. CAPM, RATING Merton, rating agency, … Merton, rating agency, … RATING
  • 55. 55 Pricing Models Pricing models are complex mathematical functions that make many assumptions: There is not such a thing as a complete Pricing Van1y: Spot price paths; HedgeFreq: 0.25 days Model. 1.8  dS = µdt + vdW  t 1.7 S Pricing models are only approximations to the real dv = κ (θ − v) dt + σdYy 1.6  price of financial products. < dWt , dYt > = ρdt 1.5 Spot price 1.4 A model does necessarily impose some 1.3 simplifications in the fundamental hypothesis. 1.2 In banking there is not a lab where models can be 1.1 tested. 1 0.9 Mar06 May06 Jun06 Aug06 Sep06 Nov06 Jan07 Feb07 Apr07 The uncertainty of the market adds some complexity to the problem. S5 p2 A great deal of expertise is required to construct S2 p0 1-p2 such pricing functions. We have proven expertise S0 S4 1-p0 p1 in the development of pricing models for all types S1 1-p1 S3 of exotic derivatives. t= δ t=δt δ t=2·δt
  • 56. 56 Pricing Models Black- Closed form Scholes Trees Calibration Numerical Monte Carlo required PDE
  • 57. 57 Pricing Models Models based on the Black-Scholes equation dS = S µ ·dt + S ·σ ·dW t Randomness factor Changes in the stock price Drift rate Time increment Scale for the Randomness factor Pros Cons Closed form solutions Constant parameters (rates, vols, dividends) Only applicable to vanilla instruments.
  • 58. 58 Pricing Models Trees S5 C5 p2 p2 S2 C2 p0 p0 1-p2 1-p2 S0 S4 C0 C4 p1 p1 1-p0 1-p0 S1 C1 1-p1 S3 1-p1 C3 t=0 δ t=δt δ t=2·δt t=0 δ t=δt δ t=2·δt Pros Cons Fast computing Numerical errors Account for temporal structure of rates, Not applicable to multiple underlying vols and dividends products Appropriate for American and Barrier options
  • 59. 59 Pricing Models Examples: Binomial tress Jarrow-Rudd (JR) Cox-Ross-Rubinstein (CRR) Trigeorgis (TRG) Sup = Snow·u Sup = Snow·u Sup = Snow·u Sdown = Snow·d Sdown = Snow·d Sdown = Snow·d 1  1 2  r −q − σ  ∆T +σ ∆T ν = r −q− σ2 u=e  2  u = eσ ∆T 2 σ 2∆T +ν 2 ∆T 2 −σ ∆T u=e  1 2  r −q − σ  ∆T −σ ∆T d =e d =e  2  d = e− σ ∆T +ν ∆T 2 2 2 ( r −q ) ∆T −σ ∆T e −e 1 p= ν∆T p= eσ ∆T − e−σ ∆T 1 1 p= + · 2 2 2 σ 2∆T +ν 2 ∆T 2 Example: Hull-White model drt = (θt − at ·rt )·dt + σ t ·dWt
  • 60. 60 Pricing Models Monte Carlo Van1y: Spot price paths; HedgeFreq: 0.25 days 1.8 1.7 1.6 1.5 Spot price 1.4 1.3 1.2 1.1 1 0.9 Mar06 May06 Jun06 Aug06 Sep06 Nov06 Jan07 Feb07 Apr07 Pros Cons Can price any instrument Requires lots of processing time Can properly capture the smile and the Needs calibration, lots of calibration market correlation parameters Ease of implementation Instabilities, specially in greeks
  • 61. 61 Pricing Models Examples: Binomial trees = rt ·dt + Γ(t, T )·dWt dB(t, T ) Heath-Jarrow-Morton B(t, T ) = r·dt + σ (t, S )·dWt dS Local Vol S  dS  = µ dt + v dWt S Stocastic Vol dv = κ (θ − v) dt + σ dYy  < dWt , dYt > = ρ dt
  • 62. 62 Pricing Models PDE S Vi- Vi+1,j+ 1,j+1 1 Vi-1,j Vi+1,j Vi,j dS Vi-1,j-1 Vi+1,j- 1 t dt Pros Cons Fast computing Numerical errors Can properly capture the smile Not applicable to multiple underlying Appropriate for American and Barrier products options
  • 63. 63 Pricing Models Example: Cheyette model dx(t ) = ( y(t ) − κ (t ) · x(t )) · dt + η(t )·dWt ( ) dy(t ) = η (t ) − 2 ·κ (t ) · y(t ) · dt 2 r(t ) = f (0, t ) + x(t )
  • 64. 64 Contact details: paco.sanchez@indizen.com ℡ + 34 615 903 579