Parametric volatility models can be seen as the result of some form of dimensionality reduction obtained by projecting the volatility surface into a basis of risk factors. Examples include polynomial models and stochastic volatility models having an explicit expression for the smile, such as the...

This textbook introduces the mathematical models and algorithms utilised in machine learning, covering supervised and unsupervised learning as well as reinforcement learning: In supervised learning we present ensemble models, artificial neural networks, deep neural networks, recurrent neural...

An option pricing model is tied to its ability of capturing the dynamics of the underlying spot price process. Its misspecification will lead to pricing and hedging errors. Parametric pricing formula depends on the particular form of the dynamics of the underlying asset. For tractability...