{'fraction_non_alphanumeric': 0.022458628841607566, 'fraction_numerical': 0.0035460992907801418, 'mean_word_length': 5.32089552238806, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Volatility Bursts: A Discrete-Time Option Model with Multiple Volatility Components

I propose an affine discrete-time model, called Vector Autoregressive Gamma with volatility Bursts (VARG-B) in which volatility experiences, in addition to frequent and small changes, periods of sudden and extreme movements generated by a latent factor which evolves according to the Autoregressive Gamma Zero process. A key advantage of the discrete-time specification is that it makes it possible to estimate the model via the Extended Kalman Filter. Moreover, the VARG-B model leads to a fully analytic conditional Laplace transform, resulting in a closed-form option pricing formula. When estimated on S&P500 index options and returns the new model provides more accurate option pricing and modelling of the IV surface compared with some alternative models.