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Model-Free Discretisation-Invariant Swap Contracts

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  • Carol Alexander
  • Johannes Rauch

Abstract

Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Hence there exist an infinite variety of other variance and higher-moment risk premia that are less prone to bias than standard variance swaps because their option replication portfolios have no discrete-monitoring or jump errors. Their fair values are also independent of the monitoring partition. A sub-class consists of pay-offs with fair values that are further free from numerical integration errors over option strikes. Here exact pricing and hedging is possible via dynamic trading strategies on a few vanilla puts and calls. An S&P 500 empirical study on higher-moment and other DI swaps concludes.

Suggested Citation

  • Carol Alexander & Johannes Rauch, 2016. "Model-Free Discretisation-Invariant Swap Contracts," Papers 1602.00235, arXiv.org, revised Apr 2016.
    • Handle: RePEc:arx:papers:1602.00235
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    References listed on IDEAS

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    Cited by:

    1. Johannes Rauch & Carol Alexander, 2016. "Tail Risk Premia for Long-Term Equity Investors," Papers 1602.00865, arXiv.org.
    2. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.

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