Currency trios - using geometric concepts to visualise and interpret relationships between currencies

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dc.contributor.advisorMahomed, Obeiden_ZA
dc.contributor.advisorPolakow, Danielen_ZA
dc.contributor.advisorVan de Linde, Gideonen_ZA
dc.contributor.authorDavidson, Abbyen_ZA
dc.date.accessioned2017-01-25T13:48:45Z
dc.date.available2017-01-25T13:48:45Z
dc.date.issued2016en_ZA
dc.description.abstractA currency trio is a set of three currencies and their respective exchange rates, which have a relationship fixed by a triangular arbitrage condition. This condition forms the basis for the derivation of a geometric interpretation of the relationships between the exchange rates. In the geometric framework, the three currencies in a currency trio are represented by a triangle, where each of the vertices represents a currency. The volatilities of the exchange rates are represented by the lengths of the sides joining the respective currencies and the cosine of each angle represents the correlation between the two exchange rates depicted by the angle's adjacent sides. The geometric approach is particularly useful when dealing with implied data as it allows the calculation of implied correlation using implied volatility. This is valuable as implied volatility is frequently quoted in the foreign exchange market; whereas, implied correlation is not directly quoted and is more difficult to extract from market data. This dissertation aims to thoroughly investigate the geometric framework and use it to visualise and interpret the relationships between currencies in a currency trio. The analysis will initially look at currency trios with realised spot data before moving on to implied data. In the implied data context, the framework will be used to extract and evaluate implied correlation estimates using implied volatility data extracted from the foreign exchange market. The framework will be extended to investigate whether an illiquid option can be proxy hedged using options on the two other currencies in a currency trio. Finally, the findings will be discussed and the feasibility of the applications of the framework will be considered.en_ZA
dc.identifier.apacitationDavidson, A. (2016). <i>Currency trios - using geometric concepts to visualise and interpret relationships between currencies</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/23029en_ZA
dc.identifier.chicagocitationDavidson, Abby. <i>"Currency trios - using geometric concepts to visualise and interpret relationships between currencies."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016. http://hdl.handle.net/11427/23029en_ZA
dc.identifier.citationDavidson, A. 2016. Currency trios - using geometric concepts to visualise and interpret relationships between currencies. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Davidson, Abby AB - A currency trio is a set of three currencies and their respective exchange rates, which have a relationship fixed by a triangular arbitrage condition. This condition forms the basis for the derivation of a geometric interpretation of the relationships between the exchange rates. In the geometric framework, the three currencies in a currency trio are represented by a triangle, where each of the vertices represents a currency. The volatilities of the exchange rates are represented by the lengths of the sides joining the respective currencies and the cosine of each angle represents the correlation between the two exchange rates depicted by the angle's adjacent sides. The geometric approach is particularly useful when dealing with implied data as it allows the calculation of implied correlation using implied volatility. This is valuable as implied volatility is frequently quoted in the foreign exchange market; whereas, implied correlation is not directly quoted and is more difficult to extract from market data. This dissertation aims to thoroughly investigate the geometric framework and use it to visualise and interpret the relationships between currencies in a currency trio. The analysis will initially look at currency trios with realised spot data before moving on to implied data. In the implied data context, the framework will be used to extract and evaluate implied correlation estimates using implied volatility data extracted from the foreign exchange market. The framework will be extended to investigate whether an illiquid option can be proxy hedged using options on the two other currencies in a currency trio. Finally, the findings will be discussed and the feasibility of the applications of the framework will be considered. DA - 2016 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2016 T1 - Currency trios - using geometric concepts to visualise and interpret relationships between currencies TI - Currency trios - using geometric concepts to visualise and interpret relationships between currencies UR - http://hdl.handle.net/11427/23029 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/23029
dc.identifier.vancouvercitationDavidson A. Currency trios - using geometric concepts to visualise and interpret relationships between currencies. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/23029en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titleCurrency trios - using geometric concepts to visualise and interpret relationships between currenciesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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