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Shortfall-Risk Hedging for Game Options with Minimum Trading Costs

Article arXiv papers · Author: Yan Dolinsky et al.
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Summary

The paper studies partial hedging of game options when each trade incurs costs equal to the greater of a proportional charge and a fixed minimum. In a continuous-time Black–Scholes setting, it proves that a trading strategy exists that minimizes shortfall risk, the risk associated with failing to meet the option obligation fully.

For computation, the authors use binomial models to construct numerical schemes for estimating shortfall risk and the associated optimal portfolio in the Black–Scholes model. The supplied description establishes an existence result and outlines a numerical approach, but gives no numerical findings, parameter choices, or comparison with other hedging methods. Its conclusions are therefore limited to the stated model and transaction-cost structure.

Key ideas

  • The setting is partial hedging of game options under transaction costs with a fixed minimum per trade.
  • In the continuous-time Black–Scholes model, a shortfall-risk-minimizing strategy exists.
  • Binomial models provide numerical schemes for estimating shortfall risk and the corresponding portfolio.
  • The document does not report numerical results or evidence beyond the specified model.

Tags

OptionsDerivatives pricingRisk managementPortfolio construction
Full text
# Risk Minimization for Game Options in Markets Imposing Minimal Transaction Costs


# Risk Minimization for Game Options in Markets Imposing Minimal Transaction Costs









We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction costs. We prove that in the continuous time Black--Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.

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.