Gamma hedging and rough paths

John Armstrong () and Andrei Ionescu
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John Armstrong: King’s College London
Andrei Ionescu: King’s College London

Finance and Stochastics, 2025, vol. 29, issue 4, No 1, 933-979

Abstract: Abstract We apply rough-path theory to study the discrete-time gamma-hedging strategy. We show that if a trader knows that the market prices of a set of European options are given by a diffusive pricing model, then the discrete-time gamma-hedging strategy enables them to replicate other European options so long as the underlying pricing signal has finite p $p$ -variation for p 1 $\frac{1}{p}+\frac{1}{q}>1$ , one can use the gamma-hedging strategy to replicate any European derivative with smooth payoff and maturity T $T$ . This is a sure result which holds without assuming any probabilistic model for the trajectory of the stock price path.

Keywords: Gamma hedging; Rough path; 91G80; 60L20 (search for similar items in EconPapers)
JEL-codes: C50 G10 G11 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-025-00576-2

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