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

 dc.contributor.advisor Mahomed, Obeid en_ZA dc.contributor.advisor Polakow, Daniel en_ZA dc.contributor.advisor Van de Linde, Gideon en_ZA dc.contributor.author Davidson, Abby en_ZA dc.date.accessioned 2017-01-25T13:48:45Z dc.date.available 2017-01-25T13:48:45Z dc.date.issued 2016 en_ZA dc.description.abstract 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. en_ZA dc.identifier.apacitation Davidson, A. (2016). Currency trios - using geometric concepts to visualise and interpret relationships between currencies. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/23029 en_ZA dc.identifier.chicagocitation Davidson, Abby. "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. http://hdl.handle.net/11427/23029 en_ZA dc.identifier.citation Davidson, 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.uri http://hdl.handle.net/11427/23029 dc.identifier.vancouvercitation Davidson 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/11427/23029 en_ZA dc.language.iso eng en_ZA dc.publisher.department Division of Actuarial Science en_ZA dc.publisher.faculty Faculty of Commerce en_ZA dc.publisher.institution University of Cape Town dc.subject.other Mathematical Finance en_ZA dc.title Currency trios - using geometric concepts to visualise and interpret relationships between currencies en_ZA dc.type Master Thesis dc.type.qualificationlevel Masters dc.type.qualificationname MPhil en_ZA uct.type.filetype Text uct.type.filetype Image uct.type.publication Research en_ZA uct.type.resource Thesis en_ZA
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