Pricing options and computing implied volatilities using neural networks
Pricing options and computing implied volatilities using neural networks
This paper presents a data-driven approach using artificial neural networks (ANNs) to accelerate the pricing of European options and the computation of implied volatilities. The method trains an optimized multi-layer perceptron on data generated by traditional numerical solvers, then uses the trained ANN as a fast surrogate. The approach is tested on three financial computing tasks: the Black-Scholes analytic solution, the COS method for the Heston stochastic volatility model, and Brent's iterative method for implied volatility. The ANN architecture, with four hidden layers of 400 neurons each and ReLU activation, is selected via random search and cross-validation. Training data is generated using Latin hypercube sampling to cover the parameter space efficiently. Numerical results demonstrate that the ANN achieves high accuracy (e.g., MSE around 10^-8 for Black-Scholes prices) while reducing computing time by several orders of magnitude, making it suitable for real-time applications like model calibration and risk management. The study highlights the potential of machine learning to replace computationally expensive numerical methods in quantitative finance without significant loss of precision.
Highlights
- 1Proposes a data-driven ANN framework to accelerate option pricing and implied volatility computation.
- 2Demonstrates ANN approximation of Black-Scholes analytic solution, Heston COS method, and Brent's root-finding for implied volatility.
- 3Achieves significant speedup in computing time while maintaining high accuracy across all tested models.
- 4Employs hyperparameter optimization via random search and cross-validation to select optimal ANN architecture.
Methods
- MMulti-layer perceptron (MLP) with 4 hidden layers, 400 neurons each, ReLU activation, trained with Adam optimizer.
- MLatin hypercube sampling for generating training data covering parameter ranges.
- MCyclical learning rate and decay learning rate schedules for efficient training.
- Mk-fold cross-validation combined with random search for hyperparameter tuning.
Results
- RANN achieves high accuracy with MSE on the order of 10^-8 for Black-Scholes option prices.
- RImplied volatility ANN yields errors below 0.1% in most regions, with slight degradation for deep ITM/OTM options.
- RHeston model option prices approximated with relative errors around 0.1% using COS-generated training data.
- RComputing time reduced by several orders of magnitude compared to traditional solvers, especially for large-scale evaluations.
- RANN generalizes well to unseen parameter combinations within the training range.
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