Improved Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Deep Learning

Core Concepts

The authors provide a fundamental theorem of asset pricing and a superhedging duality in a setting that combines dependence uncertainty with additional information on the dependence structure in the form of known prices for multi-asset options. They solve the resulting optimization problem using a penalization approach combined with a deep learning approximation.

Abstract

The article presents a hybrid approach between model-uncertainty and model-free/data-driven methods in finance. The authors consider the classical setting of dependence uncertainty, where the marginals are known but the dependence structure is unknown. They extend this setting by incorporating additional information in the form of traded multi-asset options.
The key contributions are:

Derivation of a fundamental theorem of asset pricing and a superhedging duality in this setting.
Characterization of the optimal measures and trading strategies.
Numerical method based on a penalization approach and deep learning approximation to compute the model-free bounds.
Numerical experiments using artificial data to evaluate the impact of additional information and the scalability of the method.

The numerical results show that the method is fast and accurate, and the computational time scales linearly with the number of assets. The authors also observe that "relevant" information, i.e. prices of derivatives with the same payoff structure as the target payoff, are more useful than other information and should be prioritized.

Stats

The initial values, variances and correlation matrix used in the numerical experiments are:
S0 = [10, 10, 10]
σ = [0.3, 0.4, 0.5]
ρ = [[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]]

Quotes

None

Key Insights Distilled From

Improved model-free bounds for multi-asset options using option-implied information and deep learning

by Evangelia Dr... at arxiv.org 04-04-2024

https://arxiv.org/pdf/2404.02343.pdf

Deeper Inquiries

How can the proposed method be extended to handle path-dependent derivatives or more complex payoff structures

The proposed method can be extended to handle path-dependent derivatives or more complex payoff structures by incorporating additional information and constraints into the optimization framework. For path-dependent derivatives, the method can be adapted to include historical price data or specific conditions that depend on the path of the underlying assets. This would involve modifying the payoff functions and constraints to account for the path-dependent nature of the derivatives. Additionally, more complex payoff structures can be accommodated by introducing additional traded options with corresponding payoff functions, similar to the approach taken in the study for multi-asset options. By incorporating a wider range of option-implied information and constraints, the method can be tailored to address a variety of derivative products with diverse characteristics.

What are the potential limitations or drawbacks of relying on option-implied information, especially in less liquid markets

While relying on option-implied information can provide valuable insights and enhance the accuracy of model-free bounds, there are potential limitations and drawbacks, especially in less liquid markets. One limitation is the assumption that the traded options accurately reflect the true market prices and expectations. In less liquid markets, the availability of traded options may be limited, leading to potential inaccuracies in the implied information. Additionally, the presence of market frictions, such as transaction costs or bid-ask spreads, can impact the reliability of option-implied information. Moreover, the method may be sensitive to the choice of additional information used, and the relevance of certain options in less liquid markets may be questionable. Therefore, in such scenarios, the method's effectiveness and robustness may be compromised, necessitating careful consideration and validation of the option-implied data used.

How could the insights from this study on the relative importance of "relevant" information be applied to other areas of quantitative finance, such as portfolio optimization or risk management

The insights from this study on the relative importance of "relevant" information can be applied to other areas of quantitative finance, such as portfolio optimization or risk management, to enhance decision-making processes. In portfolio optimization, prioritizing relevant information, such as prices of derivatives with similar payoff structures to the portfolio holdings, can lead to more accurate risk assessments and asset allocations. By focusing on information that directly impacts the portfolio's performance, investors can make more informed decisions and potentially improve their risk-return profiles. Similarly, in risk management, identifying and prioritizing relevant information can help in assessing and mitigating risks more effectively. By understanding which pieces of information have a greater impact on risk exposures, risk managers can tailor their strategies and hedging approaches to better protect against adverse market movements. Overall, the insights on the significance of relevant information can guide practitioners in optimizing their investment strategies and risk management processes.