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On the hedging of options on exploding exchange rates

Author

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  • Peter Carr
  • Travis Fisher
  • Johannes Ruf

Abstract

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale, modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for superreplication strategies that succeed with probability one for both currencies as numéraire. Within this context, we interpret the lack of the martingale property of an exchange rate as a reflection of the possibility that the numéraire currency may devalue completely against the asset currency (hyperinflation). Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:1:p:115-144
    DOI: 10.1007/s00780-013-0218-3
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    More about this item

    Keywords

    Foreign exchange; Pricing operator; Put-call parity; Strict local martingales; Föllmer measure; Change of numéraire; Hyperinflation; 60G99; 60H99; 91G20; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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