{'fraction_non_alphanumeric': 0.02023809523809524, 'fraction_numerical': 0.0, 'mean_word_length': 5.371212121212121, '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}}
Computing Journal: Stochastic-volatility Models with Optional Jumps

In this paper we compare different models describing the implied volatility surface. In particular we analyse in-depth the numerical properties of the Heston model and we extend it to include Jump processes. In our approach, we first identify a closed-form solution or a closest proxy of it, we then price contingent claims testing correctness and efficiency of the numerical solution against the closed-form solution, finally the numerical solution is adapted to American-option pricing.For each model, the closed-form solution is obtained from the stochastic differential equation and the numerical solution is worked out from the integropartial-differential equation. In all cases the scaling behavior and the effective parameter range in practical cases is addressed.