Overview

This book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management.

Part 1: Switching Regime Processes

The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed.

Part 2: Self-Excited Processes and Estimation

A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models.

Fractional Brownian Motion and Gaussian Fields

Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling.

Sub-Diffusions and Market Illiquidity

Two chapters focus on sub-diffusions that allow to replicate illiquidity in financial markets.

Target Audience

This book targets undergraduate students who have followed a first course of stochastic finance and practitioners such as quantitative analysts or actuaries working in risk management.