This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.

Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

We mainly study the asymptotic behavior of the worst case scenario option prices as the volatility interval in an uncertain volatility model (UVM) degenerates to a single point, and then provide an approximation procedure for the worst case scenario prices in a UVM with small volatility interval. Numerical experiments show that this approximation procedure performs well even as the size of the volatility band is not sosmall.

We examine, both from an analytical and numerical viewpoint, the uncertain volatility model by Hobson-Rogers in the framework of degenerate parabolic PDEs of Kolmogorov type.

This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.

The recent global financial crisis exposed the serious limitations of existing economic and financial models. Not only did macro models fail to predict the crisis, they seemed incapable of explaining what was happening to the economy. Policymakers felt abandoned by the conventional tools of the now obsolete Washington consensus and the World Trade Organization’s oversimplified faith in free markets.The traditional models for agricultural commodities have so far failed to take into account the uncertain character of the global agricultural economy and its ferocious consequences in food price volatility, the worst in 300 years, yielding hunger riots throughout the world. This book explores the elements which could help to close this fundamental modeling gap. To what extent should traditional models be questioned regarding agricultural commodities? Are prices on these markets foreseeable? Can their evolution be either predicted or convincingly simulated, and if so, by which methods and models? Presenting contributions from acknowledged experts from several countries and backgrounds – professors at major international universities or researchers within specialized international organizations – the book concentrates on four issues: the role of expectations and capacity of prediction; policy issues related to development strategies and food security; the role of hoarding and speculation and finally, global modeling methods. The book offers a renewed wisdom on some of the core issues in the world economy today and puts forward important innovations in analyzing these core issues, among which the modular modeling design, the Momagri model being a seminal example of it. Reading this book should inspire fruitful revisions in policy-making to improve the welfare of populations worldwide.

This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.