Nonlinear Valuation and Non-Gaussian Risks in Finance

Dilip B. Madan, Wim Schoutens

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN:
  9781316518090
• eBook ISBN:
  9781009002493
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgments
• 1 Introduction
• 2 Univariate Risk Representation Using Arrival Rates
• 3 Estimation of Univariate Arrival Rates from Time Series Data
• 4 Estimation of Univariate Arrival Rates from Option Surface Data
• 5 Multivariate Arrival Rates Associated with Prespecified Univariate Arrival Rates
• 6 The Measure-Distorted Valuation As a Financial Objective
• 7 Representing Market Realities
• 8 Measure-Distorted Value-Maximizing Hedges in Practice
• 9 Conic Hedging Contributions and Comparisons
• 10 Designing Optimal Univariate Exposures
• 11 Multivariate Static Hedge Designs Using Measure-Distorted Valuations
• 12 Static Portfolio Allocation Theory for Measure-Distorted Valuations
• 13 Dynamic Valuation via Nonlinear Martingales and Associated Backward Stochastic Partial Integro-Differential Equations
• 14 Dynamic Portfolio Theory
• 15 Enterprise Valuation Using Infinite and Finite Horizon Valuation of Terminal Liquidation
• 16 Economic Acceptability
• 17 Trading Markovian Models
• 18 Market-Implied Measure-Distortion Parameters
• References
• Index