Επιφάνειες τεκμαρτής & τοπικής μεταβλητότητας με εφαρμογές στα δικαιώματα προαίρεσης
Implied and local volatility surfaces with applications to options
KeywordsImplied volatility ; Local volatility ; Volatility surface ; FTSE top 40 ; Futures ; Διμεταβλητή συνάρτηση ; Χρόνος στη λήξη ; Τιμή εξάσκησης ; Ομαλή επιφάνεια ; Ανώμαλη επιφάνεια
Considering that the options observed in the markets are properly priced, the volatility that justifies them could be derived. This volatility corresponds to the concept of implied volatility and operates in a slightly long context, which ignores any change at individual times. This consideration comes to be covered by local volatility. In this thesis, all the necessary theoretical models regarding the estimation of these variables together with all the required assumptions are presented. Since volatility depends on two major factors, such as the option’s expiration time and the exercise price, there is now a two-variable volatility function which gives rise to the reputedly volatility surface. Based on empirical data from the Johannesburg Stock Exchange regarding options on futures on the FTSE TOP 40 INDEX with expiration within 2019, the surfaces of implied and local volatility were estimated. The results showed an expected smooth surface of implied volatility according to theory, while for the local volatility a surface with more abnormalities than expected appeared, indicating the existence of factors that influence volatility in a short-term.