Training Neural Networks to Calibrate the Heston Model
Summary
The document explains a two-stage approach to neural-network calibration of the Heston stochastic-volatility model. First, a network learns the mapping from model parameters to an implied-volatility grid. To create training examples, implied volatilities are calculated using conventional pricing methods: Heston pricing formulas, or Monte Carlo simulation for more complex models. The cited study uses many parameter settings to build its training data.
Second, the trained network is fitted to the current implied-volatility surface to estimate model parameters; this calibration step does not retrain the network. Parameter settings for the training set may be sampled from a probability distribution, though the source paper's selection method is not specified in the discussion. Thus, neural networks can make repeated calibration more efficient, but they still depend on numerically generated training targets and on suitable coverage of the parameter space. No network architecture, sampling distribution, or accuracy results are given here.
Key ideas
- Train the network to map Heston parameters to implied-volatility grids.
- Generate training targets with conventional pricing calculations or, for complex models, Monte Carlo simulation.
- After training, calibrate model inputs to the live implied-volatility surface without retraining the network.
- The discussion does not specify the cited paper's parameter-sampling scheme or report calibration accuracy.
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# Deep calibration in the Heston Model # Deep calibration in the Heston Model I am doing my master thesis on deep calibration in the Heston Model, and after reading a few academic paper (eg. Horvath et al. 2019) on the subject I understand pretty well the procedure and the motivation, however I do not understand how the authors compute the implied volatility. Do they start by computing the option prices using Heston closed form solution and than use the Black Scholes formula to obtain the implied volatility from these prices ? Also if this is the case how can you train a neural network to do so ? Do you need to compute the prices and implied volatilities numerically first to input them to train the neural networks ? Thanks in advance ## Answer by Achrbot (score 1, accepted) https://quant.stackexchange.com/a/78677 In Horvath et al. (2019), the authors split the procedure into two parts: - Training the neural network (NN) - Calibrating the network to the current IV surface. This step 'merely' determines the input parameters, and doesn't affect the NN itself. In step 1, a NN is trained to approximate the mapping from model parameters to IV. The training data consists of IV grids, across a range of model parameters (in their case 80 000 parameter settings). These IV's must be computed the 'classical' way, e.g. by Heston's formula, or for more complex models, MC simulation. AFAICT, the authors do not specify how they choose parameter settings for the training data, but a common method is to sample parameters from some probability distribution. You can check out Rømer (2022) for a in depth example, he also has a github with the trained models. Once the NN has been trained, model parameters can be efficiently estimated, by calibrating to the current IV.
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