Nonlinear Valuation and Non-Gaussian Risks in Finance

With a zero economic horizon, risk is considered an exposure to a change in state that may occur instantaneously at any time, and all activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically. This book provides a nonlinear non-Gaussian valuation framework for risk management in finance, where risk-free assets disappear, and low-risk portfolios must pay for their risk reduction with negative expected returns. Hedges can be constructed to enhance value, and machine learning algorithms can synthesize dynamic trading mechanisms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.

Format: Hardback
Length: 281 pages
Publication date: 03 February 2022
Publisher: Cambridge University Press

When the economic horizon approaches zero, risk takes on a unique dimension, as it becomes an exposure to potential changes that can occur instantaneously at any time. This transformative shift in perspective requires a reevaluation of all activities that have traditionally been analyzed statically within a fixed finite horizon. At the heart of this reimagining lies the concept of arrival rates, which assumes that future events can be modeled as a sequence of random variables with known probabilities.

In response to this paradigm shift, this book has been crafted with practitioners and researchers in financial risk in mind. It serves as a comprehensive guide that delves into the theoretical foundations and diverse applications of the newly established dynamic conic finance theory. The outcome is a nonlinear non-Gaussian valuation framework, offering a powerful tool for risk management in the realm of finance.

One of the significant consequences of a zero economic horizon is the disappearance of risk-free assets. In this context, traditional investments such as government bonds or cash become unattractive, as they offer minimal returns or even negative expected returns. To mitigate this risk, investors must seek out low-risk portfolios that are capable of reducing their exposure. However, the cost of achieving this risk reduction comes in the form of negative expected returns.

To enhance value and exploit risk interactions, hedging strategies become crucial. By combining different assets or instruments, investors can create portfolios that are less sensitive to specific market fluctuations. For instance, a combination of stocks and bonds can help balance out the risks associated with each asset class, resulting in a more stable and predictable portfolio.

Machine learning algorithms play a pivotal role in synthesizing dynamic trading mechanisms. These algorithms analyze vast amounts of data and identify patterns that can inform investment decisions. By leveraging machine learning, investors can develop optimal exposures that balance risk and reward across different strikes and maturities. This allows for more efficient and effective option positioning, enhancing the overall value of investment portfolios.

In conclusion, as the economic horizon approaches zero, risk assumes a dynamic and interconnected nature. The traditional static analysis is no longer sufficient to capture the full spectrum of potential risks and opportunities. By embracing the concept of arrival rates and employing advanced technologies such as machine learning, practitioners and researchers in financial risk can develop innovative strategies for managing risk and optimizing investment returns. This book serves as a valuable resource for those seeking to navigate the complex terrain of risk management in the modern financial landscape.

Weight: 656g
Dimension: 201 x 251 x 25 (mm)
ISBN-13: 9781316518090
Edition number: New ed