Dr. D. EgloffHead Financial Computing Zürcher Kantonalbank
Agenda Credit portfolio riskPricing of financial contracts- Next generation lattice models
- Related HPC problems and solutions
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
Agenda HPC in FinanceCredit 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
Credit Risk and Capital For a portfolio of credit exposures
Business Value
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
Emerging HPC Problems
Parallel Monte Carlo Simulation 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
Adaptive Monte Carlo Fundamental difference to non-adaptive MC - weighted samples
- non-iid sampling
- Mathematics of convergence and error analysis much more difficult
Based on stochastic optimizationParallel implementation - Communication pattern becomes more involved
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, ...
Implementation Software – Hybrid design Performance critical algorithms are implemented in C++Python is used for non-performance-critical sections
Implementation Cluster distribution Separation of risk factor dynamics and instrument valuation from statistical aggregationThe simulation process is monitored by a management nodeThe number of nodes for statistical aggregation depends on the number and type of statistics requiredCommunication through efficient MPI
Agenda HPC in FinanceCredit 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
What is Pricing? Fundamental theorem of asset pricingNo arbitrage pricing- Under suitable assumptions prices are expectations under a so called risk neutral measure
Numerical Pricing Methods AnalyticalSemi-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
Lattice Methods States mapped to a lattice
Business Value
Emerging HPC Problems
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