Perfect hedging in rough Heston models

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Perfect hedging in rough Heston models

Omar El Euch
Mathieu Rosenbaum
Published on 3/15/2017
Options
Derivatives
Risk management
Volatility effect

This paper addresses the challenge of hedging derivatives under rough volatility models, specifically the rough Heston model, which incorporates fractional Brownian motion to capture realistic volatility dynamics. Despite the complexity introduced by fractional processes, the authors demonstrate that explicit perfect hedging strategies exist. The key insight is that the replicating portfolio consists of the underlying asset and the forward variance curve, enabling theoretical perfect hedging. From a probabilistic perspective, the study reveals the infinite-dimensional Markovian structure underlying rough volatility models, providing a deeper understanding of their dynamics. This work bridges the gap between the empirical success of rough volatility and practical risk management, showing that hedging is not only possible but also tractable.

Highlights

  • 1Explicit perfect hedging strategies derived for rough Heston models.
  • 2Replicating portfolios consist of the underlying asset and forward variance curve.
  • 3Uncovers the infinite-dimensional Markovian structure of rough volatility models.
  • 4Bridges rough volatility theory with practical hedging applications.

Methods

  • M
    Infinite-dimensional Markovian representation of rough Heston models.
  • M
    Forward variance curve as a hedging instrument.
  • M
    Probabilistic analysis of fractional Brownian motion dynamics.

Results

  • R
    Perfect hedging is theoretically achievable in rough Heston models.
  • R
    Hedging strategies are explicit and involve only the underlying asset and variance curve.
  • R
    The infinite-dimensional Markovian structure is disentangled.
  • R
    Rough volatility models can be hedged despite fractional dynamics.
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