Derivative Pricing for Risk Calculations – Challenges and Approaches

1. Research Workshop on Fast Financial Algorithms and Computing Dan Travers Product Manager SunGard Adaptiv 4th July 2007 Derivative Pricing for Risk Calculations – Challenges and Approaches

2. Introduction • Capital Markets and Investment Banking • Adaptiv Product Suite – Enterprise Risk Management & Operations • Different perspective on similar problems

3. Challenges Analytics Portfolio Complexity Portfolio Size

4. Challenges Analytics Portfolio Complexity Portfolio Size • Increasing size of Portfolios • Volumes are expanding exponentially • Increasing complexity of Portfolios • Mix of exotic derivative instruments is increasing • Requirements and Incentives to use more risk-sensitive Risk Measurement techniques • Basel II allows much more risk-sensitive treatment of risks • Usually involve simulation techniques • Push for greater consistency and rigor in risk • Basel II required more validation and internal oversight

5. Market Problems 1 – Credit PFE Simulation • Potential Future Exposure (PFE) • Simulation-based Credit risk measure • Model portfolio over the lifetime of the deals • “Age” the portfolio • Apply Netting and collateral • Key metrics: • Portfolio Exposure at Confidence level • Expected Exposure • Example of how many valuations would be required per second • 100,000 trades, 50 timepoints / trade, 5000 simulations • --> 25Billion valuations • In a 5 hour window --> 1.4 Million valuations / second

6. Analytic Approximation – MC2 • Analytical Approximation of the portfolio value • Approximate each deal by quadratic polynomial in the Risk Factor driver space • Where xi are normal variates • Aggregate payoffs to portfolio level • Transform onto orthogonal set of risk factors & use PCA analysis to reduce dimensionality • Calculate quantiles from the payoff surface as a function of these independent normal variables

7. Analytic Approximation – MC2 • Fitting the quadratic models • Use Taylor expansion where possible • For non-linear instruments, fit a quadratic to risk factor shifts at defined level of shift • Expected Exposure: • More complicated:

8. MC2 – Shortcomings & Challenges • Instrument and Portfolio Factors • Highly non-linear instruments provide difficulties • Path dependent instruments are similarly challenged to fit into analytic framework • Netting and Collateral • Hybrid approach developed • Model “acceptable” part of portfolio as a quadratic surface, with the other parts of the portfolio full-priced • Apply simulations to the quadratic surface & full-priced deals • Ensure scenario consistency • Handle Netting & Collateral • Retain the quadratic approximation at low enough level to get under the netting agreements

9. MC2 - Challenges • Tested Hybrid Approach • Good, but not accurate enough to supplant full simulation • Majority of instruments have some form of path-dependency • Greatly complicated by the Ageing

10. Brute Force? • If we cannot use clever technique to reduce the load, then we must distribute the work • Grid Computing becomes the only solution • Many systems distribute, but often with little efficiency • Scalability must be excellent – 90%+ efficiency • Implemented distribution to • Minimise the data passed around the grid • Maximise the work done on individual grid nodes • Achieved results hoped for

11. Scalability Increasing volumes – Increasing Grid Increasing trade volumes – constant Grid Increasing portfolio complexity – increasing Grid Increasing number of scenarios

12. Product Coverage & Consolidation of Pricing • What about product coverage? Consolidation of Pricing • Driver: Combined Market and Credit Risk • Driver: One set of models for Front – to – Back • One validation of models Differences: • Front Office models can be slow and accurate, but risk models are fast with less accuracy • Credit Models will need to Age • Multi-grade of models should be available in same framework • Multi-grade of Market data and simulation models

13. Extensibility Model library must be • Multi-grade • Market, Credit and Front-office • Extensible • Extensible by users and by quant / developers • Transparent • Easily verifiable by outside source

14. Extensibility 2 • Extensibility • Framework must be strong & flexible • Allow anyone to add models • Externally added models execute with the same speed as native models • Models must have “Ageing” embedded in the pricing function – for Credit pricing • What about: • Path-dependent, Callable products • Many custom derivatives – infinitely customizable products across all institutions – not possible to add a generic model

15. Scripting Framework • “Scripting” framework • Model the payoff and behaviour of the instrument in a “Script” • Accompany the framework with a library of • Stochastic models • Numerical solvers • Finite Difference Grid • Monte Carlo • Tree Pricing • Relatively common feature in Front Office systems, but bringing this to risk is more difficult • Ageing is a problem • Need enough power in the scripting and solving environment to allow performance, while keeping flexibility

16. Research Workshop on Fast Financial Algorithms and Computing Dan Travers Product Manager SunGard Adaptiv 4th July 2007 Derivative Pricing for Risk Calculations – Challenges and Approaches