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Brexit Risk Implied by the SABR Martingale Defect in the EUR-GBP Smile

Author

Listed:
  • Petteri Piiroinen
  • Lassi Roininen
  • Martin Simon

Abstract

We construct a data-driven statistical indicator for quantifying the tail risk perceived by the EURGBP option market surrounding Brexit-related events. We show that under lognormal SABR dynamics this tail risk is closely related to the so-called martingale defect and provide a closed-form expression for this defect which can be computed by solving an inverse calibration problem. In order to cope with the the uncertainty which is inherent to this inverse problem, we adopt a Bayesian statistical parameter estimation perspective. We probe the resulting posterior densities with a combination of optimization and adaptive Markov chain Monte Carlo methods, thus providing a careful uncertainty estimation for all of the underlying parameters and the martingale defect indicator. Finally, to support the feasibility of the proposed method, we provide a Brexit "fever curve" for the year 2019.

Suggested Citation

  • Petteri Piiroinen & Lassi Roininen & Martin Simon, 2019. "Brexit Risk Implied by the SABR Martingale Defect in the EUR-GBP Smile," Papers 1912.05773, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1912.05773
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    References listed on IDEAS

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    1. Hanke, Michael & Poulsen, Rolf & Weissensteiner, Alex, 2018. "Event-Related Exchange-Rate Forecasts Combining Information from Betting Quotes and Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(6), pages 2663-2683, December.
    2. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
    3. Robert Jarrow & Younes Kchia & Philip Protter, 2011. "Is there a bubble in LinkedIn's stock price?," Papers 1105.5717, arXiv.org.
    4. 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.
    5. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    6. Iain J. Clark & Saeed Amen, 2017. "Implied Distributions from GBPUSD Risk-Reversals and Implication for Brexit Scenarios," Risks, MDPI, vol. 5(3), pages 1-17, July.
    7. Petteri Piiroinen & Lassi Roininen & Tobias Schoden & Martin Simon, 2018. "Asset Price Bubbles: An Option-based Indicator," Papers 1805.07403, arXiv.org, revised Jul 2018.
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