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Option Replication with Small Transaction Costs and Modified Volatility

Article arXiv papers · Author: Jiatu Cai et al.
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Summary

The document studies dynamic hedging of a European option when the underlying follows a general local volatility model and trades incur small linear transaction costs. It constructs a continuous-control adaptation of Leland’s hedging strategy, using modified volatility in the replication approach. The aim is to asymptotically replicate the option payoff while accounting for trading frictions.

The analysis establishes a central limit theorem for the hedging error and derives its asymptotic variance. It then gives an explicit trading strategy that minimizes this variance. These are theoretical asymptotic results: the excerpt does not provide the strategy’s formula, assumptions beyond the stated model and cost structure, numerical examples, or evidence about finite-sample performance. Practical use would depend on how well the local volatility specification and small-cost approximation fit the market and on how implementation constraints affect continuous rebalancing.

Key ideas

  • The setting is dynamic replication of a European option under a general local volatility model.
  • Trading incurs small linear transaction costs.
  • A continuous-control version of Leland’s strategy uses modified volatility to replicate the payoff asymptotically.
  • A central limit theorem characterizes the hedging error, and an explicit strategy minimizes its asymptotic variance.

Tags

OptionsDerivatives pricingVolatilityExecutionRisk management
Full text
# Asymptotic replication with modified volatility under small transaction costs


# Asymptotic replication with modified volatility under small transaction costs









Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An associated central limit theorem of hedging error is proved. The asymptotic error variance is minimized by an explicit trading strategy.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.