On the hedging of options on exploding exchange rates

Peter Carr, Travis Fisher () and Johannes Ruf ()

Finance and Stochastics, 2014, vol. 18, issue 1, 115-144

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

Keywords: Foreign exchange; Pricing operator; Put-call parity; Strict local martingales; Föllmer measure; Change of numéraire; Hyperinflation; 60G99; 60H99; 91G20; G13 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (30)

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Working Paper: On the Hedging of Options On Exploding Exchange Rates (2013)
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DOI: 10.1007/s00780-013-0218-3

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