Neural Networks for Derivatives Pricing & Calibration Models

“Make the model go faster” solutions cannot keep pace.

Typically, derivatives risk management groups within financial institutions run a multitude of risk scenarios that entail thousands of risk factors on huge derivatives portfolios. With millions of risk calculations, financial organizations are confronted with a daunting computational challenge.

Given that many financial derivatives are priced under complex volatility models, for which accurate analytic formulae are not available and which require slow multi-factor partial differential equations (PDEs) or Monte Carlo pricing methods, a new risk management pricing model paradigm is required.

Neural Networks are an approach that shows significant promise for accelerating the valuation of financial derivatives. Neural Networks can be used as universal function approximators.  After training on a data set generated by a rigorous, computationally intensive financial model, the trained Neural Networks can approximate the model’s results in a highly efficient manner.  Computation times may be reduced by orders of magnitude, while preserving fidelity to the rigorous model results.

SciComp, a leading provider of derivatives pricing and risk management solutions, develops Neural Network solutions for sophisticated derivatives pricing and calibration models. Drawing on our extensive experience with parallel architectures, SciComp can also provide GPU and FPGA implementations of Neural Network products for further acceleration.

Neural Network

Strategies for efficient Neural Network implementations may include:

  • Parametrizing training data sets to capture salient features in a parsimonious manner.
  • Employing existing analytic approximations or related formulae to further reduce the dynamic range of the training set.
  • Dividing global parameter space into regions, training separate networks for each.

SABR Examples

  • European futures option:
    • Train to implied volatility, deflated via approximate formula
    • Single hidden layer ANN, O(105) training data
    • RMS Implied vol and PV errors of 1bp, and 0.5bp respectively
    • 140,000 evaluations/sec
  • Double no-touch futures option:
    • Parameter space divided into regions based on estimated PV
    • Train to PV spread over Black-Scholes
    • Combined single hidden layer ANNs
    • RMS PV error of 3bp
    • 140,000 evaluations/sec

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