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- Document type:
- Masterarbeit
- Author(s):
- Neginsky, Dmitry
- Title:
- Pricing and Hedging of VIX Options
- Abstract:
- Since the early 1990s volatility indices, such as VIX by CBOE, served as market sentiment barometers as well as important pieces of information for asset allocation decisions. The later launch of first futures and exchange traded option contracts on them in 2004 and 2006, respectively, made volatility investable in an intuitive, direct and standardized way, as it did not exist before. Due to the negative correlation between volatility and the underlying market returns, investing in it can reduce market downside risks and improve portfolio efficiency. Furthermore, implicit volatility exposure can be hedged or directional trading of volatility levels is possible. In this thesis we take a look on the new calculation methodology of the VIX index as a representative of the model-free implied volatility class and discuss possible option pricing approaches within three different models. Whaley exemplarily suggests Black-76 model, whereas Gr¨unbichler & Longstaff (1996) utilize the mean-reverting CIR process to model VIX and price options on it. Both consider VIX or its futures prices as standalone objects, whose dynamics are specified directly. In the third approach the major US equity index S&P500, whose implied volatility is measured by VIX, is described by the Heston model. Taking VIX’s calculation methodology into account, the process governing VIX can then be consistently derived as the square root of the conditional expectation of the forward looking realized variance of the S&P500 returns. Especially in the last approach the introduced affine processes and their differential characteristics turn out to be crucial in deriving the characteristic function of VIX2 needed for pricing options. Following the respective pricing formulas, delta hedge ratios as well as other sensitivities are derived. Having calibrated the models, the effectiveness of the delta hedging strategy for VIX options is analysed on several market data sets. Calibration and hedging results are compared, allowing for further suggestions for practice.
- Advisor:
- Dr. Arnd Pauwels, Dr. Michael Kerber
- Referee:
- Prof. Dr. Matthias Scherer
- Date of acceptation:
- 31.03.2015
- Year:
- 2014
- University:
- Technische Universität München
- Faculty:
- Fakultät für Mathematik
- TUM Institution:
- Lehrstuhl für Finanzmathematik
- Format:
- Text
BibTeX