## Dr. D. Egloff ## Head Financial Computing ## Zürcher Kantonalbank
**Agenda** ## Credit portfolio risk ## Pricing 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 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
**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 optimization ## Parallel 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 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
**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
**What is Pricing? ** ## Fundamental theorem of asset pricing ## No arbitrage pricing - Under suitable assumptions prices are expectations under a so called risk neutral measure
**Numerical Pricing Methods ** ## Analytical ## 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
**Lattice Methods** ## States mapped to a lattice
**Business Value**
**Emerging HPC Problems**
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