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 shares of one asset St1 and (1 ) shares of another security St2 correlated with St1. The hedging instrument in this study evaluates the effectiveness of using a more liquid, correlated asset as a hedge and the hedging performance is assessed in presence and absence of transaction costs. The decision to hedge using the alternative asset is grounded in the practical constraints created by illiquidity and high transaction costs associated with the right (primary) underlying asset. We suppose that the asset is hedged against only one of St1 or St2 using varying trading frequencies, correlation coefficients and transaction costs. We calculated a decision metric, the risk adjusted value as the risk and return measure to make meaningful decisions on when to trade St1 or S . t2 The findings demonstrate that hedging the alternative asset, with reasonably smaller transaction costs than the primary asset can be better, if the correlation between them is very strong. ARTICLE HISTORY Received 8 September 2025 Accepted 16 May 2026 KEYWORDS Hedging; proportional transaction costs; underlying asset; correlated asset; illiquid; correlation; risk adjusted value; portfolio rebalancing MATHEMATICS SUBJECT CLASSIFICATION 91G20
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