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From Monte Carlo to Wall Street

From Monte Carlo to Wall Street. Dr. D. Egloff Head Financial Computing Zürcher Kantonalbank. Agenda. HPC in Finance Credit portfolio risk Credit risk and economic capital Related HPC problems and solutions Pricing of financial contracts Next generation lattice models

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From Monte Carlo to Wall Street

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  1. From Monte Carlo to Wall Street Dr. D. Egloff Head Financial Computing Zürcher Kantonalbank

  2. Agenda • HPC in Finance • Credit portfolio risk • Credit risk and economic capital • Related HPC problems and solutions • Pricing of financial contracts • Next generation lattice models • Related HPC problems and solutions

  3. HPC in Financial Service Industry • Problem domain • Risk management, particularly of rare events such as in credit and operational risk • Pricing of structured financial products • Statistical estimation and calibration of models for forecasting, pricing, risk management • Methods • Simulation (Monte Carlo and refinements) • Large scale optimisation • Large scale linear algebra • Partial differential equations • Fourier transform

  4. Agenda • HPC in Finance • Credit portfolio risk • Credit risk and economic capital • Related HPC problems and solutions • Pricing of financial contracts • Next generation lattice models • Related HPC problems and solutions

  5. Loss Risk capital Profit Less than x% ny today 1y 2y Credit Risk and Capital • For a portfolio of credit exposures • Simulate profit and loss over multiple periods • Reserve capital to cover x% of the worst outcomes

  6. Business Value

  7. The Price of Realism Realistic implementation of a credit portfolio risk solution requires • Dependent defaults of obligors • Long term view over multiple years • Inclusion of credit deterioration over time • Inclusion of contract cash flow details • Ability to aggregate and disaggregate Calculations become computationally demanding

  8. Emerging HPC Problems

  9. Parallel Monte Carlo Simulation • Monte Carlo is embarrassingly parallel • Runs efficiently on distributed memory clusters • Calculations generally not latency bound • sample generation generally takes longer than statistical analysis of samples • Simple communication pattern • send samples back to one or several master nodes for analysis • Analysis of extreme tail risks require improvements • Variance reductions • Adaptive schemes based on stochastic optimization

  10. Adaptive Monte Carlo • Use simulated samples to improve sampling distribution • Fundamental difference to non-adaptive MC • weighted samples • non-iid sampling • Mathematics of convergence and error analysis much more difficult • Based on stochastic optimization • Parallel implementation • Communication pattern becomes more involved

  11. Issues of Parallel Simulation How to statistically aggregate massive simulation data? • OLAP aggregation does not scale because of IO bandwidth limitations, in particularly if data stride is large • Single aggregation node may not be sufficient • Tree like aggregation requires more complex communication • Many to many communication scheme • Iterative algorithms required to calculate statistics • Easy for means and moments, more difficult for quantiles, marginal risk contributions, ...

  12. ImplementationSoftware – Hybrid design • Performance critical algorithms are implemented in C++ • Fast • Python is used for non-performance-critical sections • Dynamic and expressive • Very efficient development cycle • Ideal for prototyping

  13. ImplementationCluster distribution • Separation of risk factor dynamics and instrument valuation from statistical aggregation • The simulation process is monitored by a management node • The number of nodes for statistical aggregation depends on the number and type of statistics required • Communication through efficient MPI

  14. Agenda • HPC in Finance • Credit portfolio risk • Credit risk and economic capital • Related HPC problems and solutions • Pricing of financial contracts • Next generation lattice models • Related HPC problems and solutions

  15. What is Pricing? • Fundamental theorem of asset pricing • No arbitrage pricing • Under suitable assumptions prices are expectations under a so called risk neutral measure

  16. Numerical Pricing Methods • Analytical • Stringent assumptions, small model variety, most prominent Black Scholes model • Semi-analytical • Exploit special structure (affine, quadratic) • Expansion and perturbation techniques • Reduction to ODE (often Riccati) • Numerical • Monte Carlo • Trees • PDE and PIDE • Transform methods i.e., FFT, Laplace • Lattice methods

  17. Lattice Methods States mapped to a lattice Markov structure Model specification in terms of generator matrix, i.e. infinitesimal transition probabilities 5‘000 to 10‘000 states Dense matrices t2 t3 t1

  18. Business Value

  19. Emerging HPC Problems

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