• DOI:10.2139/ssrn.1795268
• Corpus ID: 51989559

A Note on Delta Hedging in Markets with Jumps

@article{Mijatovi2011ANO,
  title={A Note on Delta Hedging in Markets with Jumps},
  author={Aleksandar Mijatovi{\'c} and Mikhail Urusov},
  journal={ERN: Econometric Modeling in Financial Economics (Topic)},
  year={2011}
}

• A. Mijatović, M. Urusov
• Published 25 March 2011
• Mathematics
• ERN: Econometric Modeling in Financial Economics (Topic)

Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it perfectly replicates contingent claims. From the theoretical viewpoint, there is no reason for this to hold in models with jumps. However in practice the delta-hedging strategy is widely used and its potential shortcoming in models with jumps is disregarded since such models are typically incomplete and hence most contingent claims are non-attainable. In this note we investigate a complete model with jumps where the delta-hedging strategy is well-defined for regular payoff functions and is uniquely determined via the risk-neutral measure. In this setting we give examples of (admissible) delta-hedging strategies with bounded discounted value processes, which nevertheless fail to replicate the respective bounded contingent claims. This demonstrates that the deficiency of the delta-hedging strategy in the presence of jumps is not due to the incompleteness of the model but is inherent in the discontinuity of the trajectories.