Volatility (finance)

Statistics

Applied mathematics

Computer security

Convergence (economics)

Economics

Mathematical finance

Computer science

Mathematical optimization

Asset (computer security)

Dentistry

Large deviations theory

Weak convergence

Calculus (dental)

Mathematics

Econometrics

Stochastic volatility

Mathematical analysis

Artificial intelligence

Financial economics

Mathematical economics

Medicine

Economic growth

Artificial neural network

Class (philosophy)

Machine learning

Convolution (computer science)

Stochastic Processes and their Applications

We provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja and Dupuis (2019); Dupuis and Ellis (1997). We show in particular how this framework encompasses most rough volatility models used in mathematical finance, yields pathwise moderate deviations for the first time and generalises many recent results in the literature.

Large and moderate deviations for stochastic Volterra systems