This book investigates market manipulation in the volatility index VIX. The VIX is known as fear-gauge of the US stock market and its derivatives are an established hedge against negative market sentiment. Characteristically, the VIX is an index whose value is computed by a special formula based on relatively illiquid S&P 500 options. In contrast, derivatives on the VIX are heavily traded and are settled in cash once a month based on option prices determined in an auction. This short time frame makes the VIX vulnerable as manipulators can move the underlying option prices to an abnormal price level on purpose to receive an artificially high cash settlement. This book explores approaches to make the effects of manipulation measurable. For this purpose, four measures are deduced. The measures are based on the index fluctuation range, its intraday deviations from the opening value, the put/call ratio of the underlying options and their trading volume. The empirical results reveal strong indications of manipulation. The analysis is concluded by a discussion of alternative explanations of the results observed and a sketch on how to impede manipulation or change the VIX structure.

Text sample: Chapter 2.3, Product Evolution: First moves in the direction of today’s VIX can be found in 1987, when Brenner and Galai published their Sigma Index”. From the beginning on, it was meant to be the underlying for futures and options. Five years later, The American Stock Exchange investigated the feasibility of a volatility index, using the name Sigma Index”, proposed by Brenner and Galai, as working name. In 1993, Cboe Exchange, Inc., made a ?rst version of the VIX tradable. The original version was developed by Robert Whaley and measured the 30-days implied volatility of at-the-money options on the S&P 100. In 2003, Cboe Exchange, Inc., worked on a di?erent formula with Goldman Sachs. They extended the VIX to the S&P 500 and constructed the formula in today’s form, only neglecting weekly options, which are included in today’s form. The inclusion of the weekly options took place in 2014. Since that point in time, no changes to the VIX have been made. 2.4, Investors’ Usage and Derivatives: Cboe Exchange established (cash-settled) futures on the VIX in 2004 and options on the VIX in 2006. In particular the latter are a highly successful product with more than 800 000 contracts traded daily on average. Due to ongoing trading, Cboe Exchange calculates the index continuously in 15-second intervals and publishes it. When options and futures expire, a ?nal transaction takes place to transfer the pro?t or loss (if existing) to the bene?cial owner. This procedure is called settlement. Such derivatives on other instruments can be settled by delivering the underlying, for example the corresponding stock or commodity. When the underlying itself is delivered physically, the settlement is called physical. Such a physical settlement is not practical and does not make sense in the case of the VIX: A huge number of (illiquid) options would need to be delivered. Moreover, there is the second term in the formula containing the forward VIX level implied by index option prices, calculated on the basis of the one option with minimal di?erence between put and call price. This term is a number only and has no underlying physical instrument. For these reasons, VIX derivatives are always cash-settled. The application of cash-settlement implies that at one point in time, at which settlement takes place, a value for the VIX needs to be ?xed. For this purpose, a special procedure has been established which will be explained in section 2.6. Investors appreciate the chance to use VIX derivatives for hedging purposes: The VIX and stock prices have a strong negative correlation. Therefore, investors can enter a long position in the VIX to compensate losses in stocks. This can be ex-plained by considering the links of this connection in both directions: First, assume that investors expect higher volatility. As the VIX is highly positively correlated with volatility, the Investor would go long VIX. If volatility increases, market par-ticipants also expect higher risk premiums as compensation for possible downward changes in prices. As a result, buyers’ willingness to pay a certain price decreases and sellers are motivated to accept lower prices. The elementary principle of supply and demand implies falling stock prices. For the other way round, assume that –for some reason – stock prices start falling. Price movements always lead to higher volatility compared to prices staying at a constant level. This increasing volatility makes the VIX move upwards. In summary, there is a clear (abstract) negative cor-relation between the VIX and stock prices. This mechanisms can also be observed empirically.

• Volatilität

• Settlement

• Benchmark Design

• Expiration Day Effect

• Börsenindex

• Manipulation

• Hedge

Tim Maximilian Baumgartner, born in 1997, studied Mathematics and Economics at the University of Ulm and at Fudan University, Shanghai. During his studies, he put his focus on Finance and Discrete Mathematics. In parallel, he committed himself voluntarily, lastly as member of the Executive Board of the German Association of Student Initiatives ( Verband Deutscher Studierendeninitiativen e.V.”). He gained professional experience in Investment Banking and in a Big Four Audit Firm.