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 can be used as universal function approximators significantly accelerating the valuation of financial derivatives. 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.
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