Volatility Library

Article by: Peter Carr, Liuren Wu
Published by: NYU & Baruch College
Date: 2 Oct 2010

“Standard option pricing models specify the dynamics of the security price and the instantaneous variance rate, and derives its no-arbitrage implication for the option implied volatility surface. Market models start with an initial implied volatility surface and a diffusion specification for the implied volatility dynamics, and derive the no-arbitrage constraints on the risk-neutral drift of the dynamics. This paper proposes a new approach, which specifies the security price and the implied volatility dynamics while leaving the instantaneous variance rate dynamics unspecified. The allowable shape for the initial implied volatility surface is then derived based on dynamic no-arbitrage arguments. Two parametric specifications for the implied volatility dynamics lead to extreme tractability, as the whole implied volatility surface is determined by a quadratic equation. The paper also proposes a dynamic calibration methodology and calibrates the two models to over-the-counter currency option and equity index option implied volatility surfaces over an 11-year period. The model with lognormal implied variance dynamics generates superior performance over standard option pricing models of similar complexities. Furthermore, constructing implied volatility surfaces using our two models is 100 times faster than using traditional option pricing models.”

Full article (PDF): Link
Presentation (PDF): Link

Article by: Edward Szado, CFA
Published by: Isenberg School of Management
Date: Jun 2009

“In 2008, the S&P 500 experienced a drawdown of about 50% from peak to trough. Many assets
which are typically considered effective equity diversifiers also faced precipitous losses. Most
hedge fund strategies and commodity indices were not immune from declining. For example,
the HFRX Global Hedge Fund Index had a maximum drawdown of approximately 25% of its
value in 2008, with some of its sub-indexes dropping almost 60%. The drop in commodities was
even more significant. The S&P GSCI commodity index experienced a maximum drawdown of
about 2/3 of its value in 2008. In stark contrast, volatility levels as measured by VIX experienced
significant increases and in 2008 repeatedly set new highs not seen since the crash of 1987.
Exhibit 1 provides a graphic illustration of the relative performance of a collection of diverse
assets from March 2006 to December 2008. The rapid rise of VIX futures in the end of 2008
strongly contrasts with the precipitous drop in almost all the other asset classes (managed
futures is an obvious exception). This anecdotal evidence leads one to wonder if some degree
of long VIX exposure would have provided effective diversification during the market meltdown
in which the standard diversifiers mentioned above failed to provide their expected
diversification benefits.

“Prior to the financial crisis of 2008, correlations between equities, bonds and alternative assets
tended to be relatively low. However, in 2007 and 2008 the correlations for many asset classes
rose significantly as a variety of assets dropped in value alongside the drop in equities. As a
result, many investors discovered that portfolios which they believed to be well diversified based
on historical data, were effectively not diversified at all. Exhibit 2 provides an illustration
of this phenomenon. The correlations with equity were often dramatically higher in the 2007 to
2008 period than in the 2004 to 2006 period. With the exception of managed futures, all
correlations were at least moderately higher in the latter period.”

Full article (PDF): Link

Article by: Jim Fink
Published by: Seeking Alpha
Date: 23 May 2012

“Because VIX calls are based on VIX futures instead of the more volatile “spot” VIX, in the past I suggested that it would be easier to hedge a portfolio against a “black swan” stock market decline using S&P 500 puts-either the cash-settled SPX index puts or the equity-settled SPY ETF puts.

“Well, I stand corrected. In preparing for a conference down in beautiful Palm Beach, Florida, I read two academic studies-one published in 2009 and another published in 2012-that found VIX calls to be a much more effective portfolio hedge than S&P 500 puts. The reason is that most institutional investors (including mutual funds, hedge funds and pension funds) are benchmarked against the S&P 500 and have historically hedged their portfolios almost exclusively by purchasing S&P 500 puts. This institutional buying pressure has bid up their prices dramatically and made S&P 500 puts very expensive hedges for the rest of us. The more expensive a hedge, the less effective it is. By contrast, VIX calls have only been around since February 2006 and have yet to be widely adopted by “big money” institutions. Consequently, the prices of VIX calls have not been bid up by institutions and remain reasonable.”

Full article: Link

Article by: Izabella Kaminska
Published by: Financial Times
Date: 24 Feb 2012

“It’s official – volatility is back. The Vix index, which is derived from the value of S&P 500 options, posted its biggest two-day increase in nine months on Wednesday following a sharp fall in S&P 500 equities.

“All of which is good news for the CBOE, the keeper of the Vix futures contract.

“The product is viewed by the option specialist as one of its key growth areas, contributing to the bulk of the group’s performance over the past year.

“What is interesting though is that the biggest increase in Vix futures volumes happened over the course of last year when volatility was largely low.”

Full article (requires subscription): Link