Description : Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Description : This volume critically re-examines the profession's understanding of asset bubbles in light of the global financial crisis of 2007-09. It is well known that bubbles have occurred in the past, with the October 1929 crash as the most demonstrative example. However, the remarkably well-behaved performance of the US economy from 1945 to 2006, and, in particular during the Great Moderation period of 1984 to 2006, assured the economics profession and monetary policymakers that asset bubbles could be effectively managed with little or no real economic impact. The recent financial crisis has now triggered a debate about the emergence of a sequence of repeated bubbles in the Nasdaq market, housing market, credit market, and commodity markets. The realities of the crisis have intensified theoretical modeling, empirical methodologies, and debate on policy issues surrounding asset price bubbles and their potentially adverse economic impact if poorly managed. Taking a novel approach, the editors of this book present five classic papers that represent accepted thinking about asset bubbles prior to the financial crisis. They also include original papers challenging orthodox thinking and presenting new insights. A summary essay highlights the lessons learned and experiences gained since the crisis.
Description : The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.