On the hedging of options on exploding exchange rates

Peter Carr, Travis Fisher, Johannes Ruf

Research output: Contribution to journalArticle

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).

Original languageEnglish (US)
Pages (from-to)115-144
Number of pages30
JournalFinance and Stochastics
Volume18
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Change of numéraire
  • Foreign exchange
  • Föllmer measure
  • Hyperinflation
  • Pricing operator
  • Put-call parity
  • Strict local martingales

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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