What happens to risk as the economic horizon goes to zero and risk is seen as an exposure to a change in state that may occur instantaneously at any time? All activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically at a zero time horizon, with arrival rates at the core of the modeling. This book, aimed at practitioners and researchers in financial risk, delivers the theoretical framework and various applications of the newly established dynamic conic finance theory. The result is a nonlinear non-Gaussian valuation framework for risk management in finance. Risk-free assets disappear and low risk portfolios must pay for their risk reduction with negative expected returns. Hedges may be constructed to enhance value by exploiting risk interactions. Dynamic trading mechanisms are synthesized by machine learning algorithms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.

The book draws on current research on model risk and parameter sensitivity of securitisation ratings. It provides practical ideas and tools that can facilitate a more informed usage of securitisation ratings. We show how global sensitivity analysis techniques can be used to better analyse and to enhance the understanding of the uncertainties inherent in ratings due to uncertainty in the input parameters. The text introduces a novel global rating approach that takes the uncertainty in the ratings into account when assigning ratings to securitisation products. The book also covers new prepayment and default models that overcome flaws in current models. "

The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relatiions between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic anlaysis for birth-death processes and diffusions, martingale relations for Lévy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play.
This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis.
Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium.

This book explores the emerging field of risk management and risk analysis of cryptocurrencies, an area that has been generating considerable research. It begins by providing an introduction to digital finance and the concept of cryptocurrencies and blockchain technologies. It then describes in detail the intrinsic risks involved in cryptocurrencies, an area that, to date, has not been fully documented or investigated. Lastly, it discusses the various types of risk, with a focus on design, operational, market and quantitative risks. Providing insights into the analysis and management of cryptocurrencies, and serving as a starting point for a more in-depth risk analysis, this book will appeal to professionals and researchers interested in familiarizing themselves with the risks in cryptocurrencies, including academics, portfolio managers, risk-managers, quants, financial professionals, regulators, economists, asset managers and traders.

This book provides an overview of the risk components of CoCo bonds. CoCos are hybrid financial instruments that convert into equity or suffer a write-down of the face value upon the appearance of a trigger event. The loss-absorption mechanism is automatically enforced either via the breaching of a particular accounting ratio, typically in terms of the Common Equity Tier 1 (CET1) ratio, or via a regulatory trigger. CoCos are non-standardised instruments with different loss-absorption and trigger mechanisms. They might also contain additional features such as the cancellation of coupon payments. Different pricing models are discussed in detail. These models use market data such as share prices, CDS levels and implied volatility in order to calculate the theoretical price of a CoCo bond and its sensitivities, providing the investor with insides to hedge from adverse changes in the market conditions. The audience are professionals as well as academics who want to learn how to risk manage CoCo bonds using cutting edge techniques as well as all the risk involved in CoCo bonds.

This is a comprehensive introduction to the brand new theory of conic finance, also referred to as the two-price theory, which determines bid and ask prices in a consistent and fundamentally motivated manner. Whilst theories of one price classically eliminate all risk, the concept of acceptable risks is critical to the foundations of the two-price theory which sees risk elimination as typically unattainable in a modern financial economy. Practical examples and case studies provide the reader with a comprehensive introduction to the fundamentals of the theory, a variety of advanced quantitative models, and numerous real-world applications, including portfolio theory, option positioning, hedging, and trading contexts. This book offers a quantitative and practical approach for readers familiar with the basics of mathematical finance to allow them to boldly go where no quant has gone before.