the role of mathematical models in the current financial crisis athula alwis
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Athula Alwis, Senior Vice President, Global Credit, Surety and Political Risk Practice February 12, 2009
Robert Merton“At times we can lose sight of the ultimate purpose of the models when their mathematics become too interesting. The mathematics of financial models can be applied precisely, but
the models are not all precise in their application to the complex real world.
Their accuracy as a useful approximation to that world varies significantly across time and place. The models should be applied in practice only tentatively, with careful
assessment of their limitations in each application.”
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The Role of Mathematical Models in the Current Financial Crisis – Lessons for the Export Credit and
Political Risk Business
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Agenda
I. IntroductionII. Liquidity CrisisIII. Credit CrisisIV. Mortgage CrisisV. History of Mathematical ModellingVI. The Role of Models in the Current CrisisVII. What can we learn?
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Introduction
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Introduction
Source: Creators Syndicate
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Introduction
Source: Creative Commons
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Introduction
Source: Creative Commons
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Introduction
Source: Wikimedia Commons; “http://en.wikipedia.org/wiki/Image:Subprime_Crisis.jpg”
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Introduction
€ 320 billion
$ 700 billion +
£150 billion
€ 500 billionEurope $2.3 trillion in total
¥ 10 trillion
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Introduction
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Introduction
Unemployment Rates
Japan: 3.9% (Dec 2008)UK: 6.0% (Dec 2008)USA: 7.2% (Jan 2009; projected to exceed 10.0%)Germany: 7.6% (Jan 2009)France: 7.9% (Dec 2008)
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Introduction
Projected Business Failures in 2009
Japan: 17,000UK: 38,000USA: 62,000France: 63,000
Source: Financial Times and Euler Hermes
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Liquidity Crisis
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Liquidity Crisis
When an entity experiences a shortage of cashTo pay for day-to-day business operations (e.g., Payroll)To meet debt obligations on timeTo expand inventory and production
Does not necessarily mean that the business is insolvent
A specific liquidity risk!
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Liquidity Crisis
When businesses in general experience shortages of cashDue to reduced lending by banksDue to tighter lending standards by banksDue to shortage of cash at banks
A liquidity crisis!
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Liquidity Crisis
Comparison to credit crisisA sound business can experience a liquidity crisis by temporary inaccessibility to required financingA credit crisis is based on insolvency of entities• Due to steep decline of previously over-priced assets
(mortgage-backed securities, CDO, etc)
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Credit Crisis
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Credit Crisis
A material reduction in available credit and / or A significant increase in cost of credit
Widening of credit spreadsIncrease in credit default ratesWeak corporate financialsUnstable capital bases
leading to…
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Credit Crisis
Crisis of insolvencyAnticipated decline in value of collateralIncreased perception of riskChange in monetary conditionsLoss of capital at banks
Lack of confidence in financial markets!
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Mortgage Crisis
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Mortgage Crisis
CDO
Equity Tranche
Mezzanine Senior Tranche
Commercial Paper
SPE MBS
BANK
MORTGAGE LENDER
SIV
BORROWER
HIGH RISK INVESTOR
LOW RISK INVESTOR
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Mortgage Crisis
Key DriversHousing marketUnemploymentInterest rates
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Mortgage Crisis
The cost to economyRecessionLack of financing for solvent companies and individuals with good creditOver 2M job losses so far in the US in 2008 (4.5M overall)Over 2.8M unemployed in the UK
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Mortgage Crisis
The cost to financial institutionsLack of confidence• Bear Stearns and Merrill Lynch acquired• Lehman Brothers – Chapter 11 • Washington Mutual acquired• Goldman Sachs and J P Morgan became banks to survive• Concerns at Citibank and AIG• Issues at RBS
Lack of capital for growth
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Mortgage Crisis
Other concernsMortgage equity loansStudent loansCredit cardsCorporate real estate
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Mortgage Crisis
Exacerbation of the credit cycleMajor corporate failuresHigh unemploymentStagflation (inflation and economic stagnation)Recession
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Mortgage Crisis – Perfect Storm
Liquidity crisisCredit crisisMortgage crisisRecessionIt may not be over!
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History of Mathematical Modelling
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Brief History of Credit Modeling
Ancient Romans traded options against outgoing cargo from seaports
Charles Castelli (1877): Book titled “The Theory of Options in Stocks and Shares”
Louis Bachelier (1900): Earliest known analytical valuation for options in his mathematics dissertation at Sorbonne
Paul Samuelson (1955): Brownian Motion in the Stock Market
Resource: A Study of Option Pricing Models, Kevin Rubash, Foster College of Business Administration, Bradley University
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Brief History of Credit Modeling
Richard Kruizenga (1955): Put and Call Options: A Theoretical and Market Analysis
James Boness (1962): A Theory and Measurement of Stock Option ValueA clear theoretical improvement from previous work and a precursor to …
Black Scholes (1973): Option pricing Model
Resource: A Study of Option Pricing Models, Kevin Rubash, Foster College of Business Administration, Bradley University
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Brief History of Credit Modeling
Fischer Black Myron Scholes Robert Merton
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Brief History of Credit Modeling
Robert Merton (1973): Relaxed the assumption of no dividends
Jonathan Ingerson (1976): Relaxed the assumption of no taxes or transaction costs
Robert Merton (1976): Relaxed the restriction of constant interest rates
This is the beginning of structural modeling!
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Brief History of Credit Modeling
Vasicek – Kealhofer (1989): Modified Structural model
Jarrow – Turnbull (1995): Reduced Form model
Duffie – Singleton (1999): Improved Reduced Form model
David Li (2001): Incorporated a Gaussian Copula to tackle correlation
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History of Mathematical Modeling
Benefits of Modeling
To be disciplined in risk selection and management
To be strategic in managing and growing the business
To compare against other businesses in terms of risk and rewards
To measure and manage risk in a consistent manner
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History of Mathematical Modeling
Benefits of Modeling
To question and investigate assumptions, gut instincts and “what if” scenarios
To assist in increasing shareholder value
To protect the franchise
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The Role of Models in the Current Crisis
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The Role of Models in the Current Crisis
A heavy reliance on mathematical models by banks, investors and rating agencies
The use of inappropriate models to represent complex market conditions
Over reliance on unrealistic models
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The Role of Models in the Current Crisis
Use of incorrect ratings from rating agencies
Improper calibration of models (lack of reliable data, wrong assumptions, parameter error)
The mechanical use of models without properly understanding underlying data, assumptions and economic implications
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The Role of Models in the Current Crisis
Use of single metric to make decisions (For ex. Using VaR to measure one boundary of risk)
Lack of awareness of boundaries/break points (for ex. real estate values are bounded by income)
The limitations of models were not readily evident
Provided false confidence that encouraged additional risk taking by practitioners
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The Role of Models in the Current Crisis
Lack of real world business experience by model users/builders
Supported decision making solely based on past patterns
Models failed to capture liquidity risk, concentration risk, correlation risk
Lack of appreciation for systemic risk and interconnectedness of financial markets at moments of extreme stress
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What Can We Learn?
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What Can We Learn
A mathematical model is a tool. It cannot and should not replace the practitioner's experience, judgment and business intuition. The major strategic decisions should be guided by business knowledge and common sense of experienced business leaders not by models.
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What Can We Learn
A model must reflect business realities as closely as possible. Using inappropriate models mechanically without exploring the applicability has been a serious issue that must be addressedMultiple metrics and models should be employed, if possible (VaR, CTE, Volatility, Scenario Testing, …)
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What Can We Learn
The assumptions used in any model should be validated by business practitioners. It is imperative that analysts and modelers understand the market conditions, coverage and business processes rather than independently selecting assumptions for models in a vacuumThe simplifying assumptions should be evaluated for validityUse actual original data (a clear advantage for the export credit and political risk industry)
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What Can We Learn
The data that go into models should be validated, scrubbed and compared to at least one other independent source.Regular review/upgrade of models and underlying technologies has to be carried outModel correlation (risk is not randomly distributed; cannot escape it)Consider systemic risk
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What Can We Learn
Mathematical tools cannot precisely model human behavior
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Q & A