Hawkes Processes have been finding more applications in diverse areas of science, engineering and quantitative finance. In multi-frequency finance, various phenomena have been observed, such as shocks, crashes, volatility clustering, turbulent flows and contagion. Hawkes processes have been...

We employ neural networks to understand volatility surface movements. We first use daily data on options on the S&P 500 index to derive a relationship between the expected change in implied volatility and three variables: the return on the index, the moneyness of the option, and the remaining...