 A Leland model for delta hedging in central risk booksJohannes Muhle‐Karbe, Zexin Wang and Kevin Webster Mathematical Finance, 2023, vol. 33, issue 3, 504-547 Abstract: Using a tractable extension of the model of Leland (1985), we study how a delta‐hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market‐making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous‐time limit, the optimal limit‐order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid–ask spreads, and volatilities. The corresponding option price—from which the option can be replicated using market and limit orders—is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced‐form models are competitive with “brute force” numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real‐life high frequency data. Date: 2023 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:33:y:2023:i:3:p:504-547 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical Finance is currently edited by Jerome Detemple More articles in Mathematical Finance from Wiley Blackwell |
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