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Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities
This paper addresses arbitrage-free FX smile construction from near-term implied volatility dynamics proposed by Carr (J Financ Econ, 120(1), 1–20, 2016). The approach is directly applicable to FX option market conventions. Prices of market benchmark contracts (risk reversals and butterflies) are id...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer US
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9483449/ http://dx.doi.org/10.1007/s11147-022-09189-9 |
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author | Muck, Matthias |
author_facet | Muck, Matthias |
author_sort | Muck, Matthias |
collection | PubMed |
description | This paper addresses arbitrage-free FX smile construction from near-term implied volatility dynamics proposed by Carr (J Financ Econ, 120(1), 1–20, 2016). The approach is directly applicable to FX option market conventions. Prices of market benchmark contracts (risk reversals and butterflies) are identified as the roots of a cubic polynomial and ATM-volatility can be matched by construction. Implied volatilities are computed with respect to (non-premium adjusted) option deltas. The approach is compared to the Vanna Volga Approach, which does not guarantee arbitrage-free prices. An empirical application to a normal and a stress scenario demonstrates that arbitrage-free implied volatilities coincide with those from the Vanna Volga Approach when prices are interpolated between the [Formula: see text] 25-call and [Formula: see text] 25-put options. Differences are observed when implied volatilities are extrapolated to the wings. Empirically, these differences are particularly relevant in a stress scenario during the Coronavirus crises (2020). |
format | Online Article Text |
id | pubmed-9483449 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-94834492022-09-19 Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities Muck, Matthias Rev Deriv Res Article This paper addresses arbitrage-free FX smile construction from near-term implied volatility dynamics proposed by Carr (J Financ Econ, 120(1), 1–20, 2016). The approach is directly applicable to FX option market conventions. Prices of market benchmark contracts (risk reversals and butterflies) are identified as the roots of a cubic polynomial and ATM-volatility can be matched by construction. Implied volatilities are computed with respect to (non-premium adjusted) option deltas. The approach is compared to the Vanna Volga Approach, which does not guarantee arbitrage-free prices. An empirical application to a normal and a stress scenario demonstrates that arbitrage-free implied volatilities coincide with those from the Vanna Volga Approach when prices are interpolated between the [Formula: see text] 25-call and [Formula: see text] 25-put options. Differences are observed when implied volatilities are extrapolated to the wings. Empirically, these differences are particularly relevant in a stress scenario during the Coronavirus crises (2020). Springer US 2022-09-18 2022 /pmc/articles/PMC9483449/ http://dx.doi.org/10.1007/s11147-022-09189-9 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Muck, Matthias Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title | Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title_full | Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title_fullStr | Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title_full_unstemmed | Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title_short | Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities |
title_sort | arbitrage-free smile construction on fx option markets using garman-kohlhagen deltas and implied volatilities |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9483449/ http://dx.doi.org/10.1007/s11147-022-09189-9 |
work_keys_str_mv | AT muckmatthias arbitragefreesmileconstructiononfxoptionmarketsusinggarmankohlhagendeltasandimpliedvolatilities |