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

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

Challenges

 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

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

Analytic Approximation – MC 2  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

Analytic Approximation – MC 2  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:

MC 2 – 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

MC 2 - 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

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

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

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

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

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

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

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