The thesis describes and applies two parametric option pricing models which partially ease the well-known discrepancy between real world and Black-Scholes model. Stochastic volatility and jumps encompassed by Heston and SVJ models explain implied volatility smile and its heterogeneous term-structure. Both models are calibrated to market data observed for EURUSD currency options on January 23, 2015. While SVJ model provided a better fit for the market, especially for mid-term expiry smile curvature, its estimated risk-neutral parameters were unrealistic comparing with their counterparts under statistical measure. Estimations suggest zero long term price volatility and 2 jumps during the year with average magnitude of 6 \%. Both models failed to match curvature of short time to expiry smile and provided a good fit of term-structure and long-expiry smile. Analysing delta ratios adjusted for non-constant volatility as a possible alternatives the study considered minimum variance delta estimated with Heston model, delta ratio recommended by Nassim Taleb and two deltas adjusted for local volatility assuming sticky moneyness and sticky tree dynamics of implied volatility. On data set of EURUSD options from 1.1.2014 to 30.5.2015, our research did not find any alternative which would be more reliable than common Black-Scholes delta.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:206214 |
| Date | January 2014 |
| Creators | Stolbov, Anatoly |
| Contributors | Witzany, Jiří, Fičura, Milan |
| Publisher | Vysoká škola ekonomická v Praze |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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