Pathwise estimation and inference for diffusion market models discusses contemporary techniques for inferring, from options and bond prices, the market participants' aggregate view on important financial parameters such as implied volatility, discount rate, future interest rate, and their uncertainty thereof. The focus is on the pathwise inference methods that are applicable to a sole path of the observed prices and do not require the observation of an ensemble of such paths. This book is pitched at the level of senior undergraduate students undertaking research at honors year, and postgraduate candidates undertaking Master’s or PhD degree by research. From a research perspective, this book reaches out to academic researchers from backgrounds as diverse as mathematics and probability, econometrics and statistics, and computational mathematics and optimization whose interest lie in analysis and modelling of financial market data from a multi-disciplinary approach. Additionally, this book is also aimed at financial market practitioners participating in capital market facing businesses who seek to keep abreast with and draw inspiration from novel approaches in market data analysis. The first two chapters of the book contains introductory material on stochastic analysis and the classical diffusion stock market models. The remaining chapters discuss more special stock and bond market models and special methods of pathwise inference for market parameter for different models. The final chapter describes applications of numerical methods of inference of bond market parameters to forecasting of short rate. Nikolai Dokuchaev is an associate professor in Mathematics and Statistics at Curtin University. His research interests include mathematical and statistical finance, stochastic analysis, PDEs, control, and signal processing. Lin Yee Hin is a practitioner in the capital market facing industry. His research interests include econometrics, non-parametric regression, and scientific computing.

A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

The range of Bayesian inference algorithms and their different applications has been greatly expanded since the first implementation of a Kalman filter by Stanley F. Schmidt for the Apollo program. Extended Kalman filters or particle filters are just some examples of these algorithms that have been extensively applied to logistics, medical services, search and rescue operations, or automotive safety, among others. This book takes a look at both theoretical foundations of Bayesian inference and practical implementations in different fields. It is intended as an introductory guide for the application of Bayesian inference in the fields of life sciences, engineering, and economics, as well as a source document of fundamentals for intermediate Bayesian readers.

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.

Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.