From Monte Carlo to Wall Street Dr. D. Egloff



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From Monte Carlo to Wall Street

  • Dr. D. Egloff

  • Head Financial Computing

  • Zürcher Kantonalbank


Agenda

  • HPC in Finance

  • Credit portfolio risk

  • Pricing of financial contracts

    • Next generation lattice models
    • Related HPC problems and solutions


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


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

  • 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


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


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++

    • Fast
  • 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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