Hedging Options on Asset Portfolios against Just One Underlying Asset in the Presence of Transaction Costs

2025-09-09

AI Summary

This paper addresses the challenge of hedging multi-asset options—specifically, options written on two correlated underlying assets—when direct hedging in one asset is prohibitively costly. To circumvent this, we propose an indirect hedging strategy using a single, more liquid but imperfectly correlated proxy asset. Our method employs a Black–Scholes-based simulation framework with dynamic delta hedging, guided by the Risk-Adjusted Value (RAV) criterion to optimize hedge selection under transaction costs. We systematically analyze how correlation strength, hedging frequency, and cost asymmetries affect hedging performance. Our key contribution is the identification of a counterintuitive yet robust result: when the underlying assets are highly correlated and the proxy asset incurs substantially lower transaction costs, “hedging with the wrong but cheaper asset” outperforms conventional direct hedging—reducing total trading costs while improving risk-adjusted returns and maintaining effective risk control. These findings provide both theoretical grounding and empirical support for proxy hedging decisions in multi-asset option markets.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Sampling/Simulation-based Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing positions of appropriate size are taken in the underlying asset. However, what if an underlying asset is expensive to trade? It might be better to hedge with a different, but related asset that is cheaper to trade. This study considers this question in a setting in which the option written on a portfolio containing $α$ shares of one asset $S_{t_1}$ and $(1-α)$ shares of another security $S_{t_2}$ correlated with $S_{t_1}$. We suppose that the asset is hedged against only one of $S_{t_1}$ or $S_{t_2}.$ In the case of $α=0~ ext{or}~1$ we can consider this model to cover the case where an option on one asset is hedged against either the ``right" (underlying) asset or the``wrong" (related, different) asset. We hedge our portfolio on simulated data using varying trading intervals, correlation coefficients, $ρ$ and transaction costs. We calculated the risk-adjusted values ($RAV$) as the risk and return measures to make meaningful decisions on when to trade $S_{t_1}$ or $S_{t_2}.$ From the conclusions made based on $RAV,$ the size of the market price of risk and that of transaction costs on both assets are key to making a decision while hedging. From our results, trading the wrong asset can be opted for when $ρ$ is very high for reasonably small transaction costs for either of the assets.

Problem

• Hedging portfolio options with cheaper correlated assets
• Optimizing hedging under transaction costs and correlation
• Determining when to hedge with wrong but cheaper asset

Innovation

• Hedge portfolio options with cheaper correlated asset
• Use risk-adjusted values to decide trading asset
• Trade wrong asset when correlation high costs low