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To what degree is the VIX benchmark computed by CBOE representative of its definition?

Liedbeck, Patrik and Ålander, Wilhlem (2018) MASK01 20181
Mathematical Statistics
Abstract
The purpose of this paper is through an empirical approach understand the
dynamics of VIX and investigate to what degree the benchmark computed by
CBOE is representative of its definition. The method implemented is of a design
where one constructs a hypothetical world in which synthetic options data are
produced by the Bates-Heston model. This implies an underlying and known
volatility with chosen parameters κ and θ for which a theoretical reference VIX
can be produced and compared with the VIX benchmark following CBOE´s
computational method. Furthermore the thesis investigates a real life manip-
ulative accusation of the VIX. The investigation relies heavily on the moral
hazard occurring when the manipulation is done by the book.... (More)
The purpose of this paper is through an empirical approach understand the
dynamics of VIX and investigate to what degree the benchmark computed by
CBOE is representative of its definition. The method implemented is of a design
where one constructs a hypothetical world in which synthetic options data are
produced by the Bates-Heston model. This implies an underlying and known
volatility with chosen parameters κ and θ for which a theoretical reference VIX
can be produced and compared with the VIX benchmark following CBOE´s
computational method. Furthermore the thesis investigates a real life manip-
ulative accusation of the VIX. The investigation relies heavily on the moral
hazard occurring when the manipulation is done by the book.
The investigation yielded an in-depth derivation of the VIX index definition
using the Bates-Heston model coupled with Carr’s formula. The results further
showed that the CBOE computed VIX and theoretical reference VIX coincide
with the greatest deviation occurring with a value slightly greater than 0.02,
arguing for the CBOE computed VIX to be representative of its definition. Al-
though the manipulation might not be as easy as one might think. The vast
structure of the VIX calculations makes it hard trying to force arbitrage oppor-
tunities. (Less)
Popular Abstract (Swedish)
VIX indexet, även kallat "the fear gauge" är världens ledande indikator för
framtida volatilitet. Indexet beräknar ett 30 dagars framtida förväntat värde på
volatiliteten kring USA’s börs S&P500. Indexet baseras på köp och säljoptioner
med S&P500 indexet som underliggande tillgång. Optionerna som används in-
nehar två olika löptider som vi kallar för nära och nästa periods-optioner.
Uppsatsen baseras på en fiktiv värld där artificiell optionsdata genereras från
Hestonmodellen. Utöver Hestons modell härleds flera olika tillvägagångssätt för
att prissätta Europeiska derivat, bland andra Bates och Carr’s formler samt
deras likheter med Hestons modell.
Metoden skildrar en empirisk studie av Chicago Board of Exchange’s beräkningar
med... (More)
VIX indexet, även kallat "the fear gauge" är världens ledande indikator för
framtida volatilitet. Indexet beräknar ett 30 dagars framtida förväntat värde på
volatiliteten kring USA’s börs S&P500. Indexet baseras på köp och säljoptioner
med S&P500 indexet som underliggande tillgång. Optionerna som används in-
nehar två olika löptider som vi kallar för nära och nästa periods-optioner.
Uppsatsen baseras på en fiktiv värld där artificiell optionsdata genereras från
Hestonmodellen. Utöver Hestons modell härleds flera olika tillvägagångssätt för
att prissätta Europeiska derivat, bland andra Bates och Carr’s formler samt
deras likheter med Hestons modell.
Metoden skildrar en empirisk studie av Chicago Board of Exchange’s beräkningar
med den teoretiska härledningen av indexet. Uträkningarna jämförs sedan med
de aktuella värdena på S&P500 indexet för att få maximal förståelse kring in-
dexets dynamik.
Avslutningsvis undersöks ett verkligt scenario från en neutral ståndpunkt av
påstådd manipulering av VIX. (Less)
Please use this url to cite or link to this publication:
author
Liedbeck, Patrik and Ålander, Wilhlem
supervisor
organization
course
MASK01 20181
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
8950672
date added to LUP
2018-06-18 11:13:30
date last changed
2018-06-18 11:13:30
@misc{8950672,
  abstract     = {The purpose of this paper is through an empirical approach understand the
dynamics of VIX and investigate to what degree the benchmark computed by
CBOE is representative of its definition. The method implemented is of a design
where one constructs a hypothetical world in which synthetic options data are
produced by the Bates-Heston model. This implies an underlying and known
volatility with chosen parameters κ and θ for which a theoretical reference VIX
can be produced and compared with the VIX benchmark following CBOE´s
computational method. Furthermore the thesis investigates a real life manip-
ulative accusation of the VIX. The investigation relies heavily on the moral
hazard occurring when the manipulation is done by the book.
The investigation yielded an in-depth derivation of the VIX index definition
using the Bates-Heston model coupled with Carr’s formula. The results further
showed that the CBOE computed VIX and theoretical reference VIX coincide
with the greatest deviation occurring with a value slightly greater than 0.02,
arguing for the CBOE computed VIX to be representative of its definition. Al-
though the manipulation might not be as easy as one might think. The vast
structure of the VIX calculations makes it hard trying to force arbitrage oppor-
tunities.},
  author       = {Liedbeck, Patrik and Ålander, Wilhlem},
  language     = {eng},
  note         = {Student Paper},
  title        = {To what degree is the VIX benchmark computed by CBOE representative of its definition?},
  year         = {2018},
}