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Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits

27 Jun 2012

Article by: Asli Oztukel
Published by: Mathematical Institute, Oxford
Date: 1999

“In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide ‘confidence limits’ for the option value.”

Full article (PDF): Link

 
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Posted in Realized volatility

 

VIX Futures and Options – A Case Study of Portfolio Diversification During the 2008 Financial Crisis

05 Jun 2012

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

 
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Posted in Implied volatility

 

Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility

25 May 2012

Article by: Andrew J. Patton, Kevin Sheppard
Published by: Duke University
Date: 7 Oct 2011

“Using recently proposed estimators of the variation of positive and negative returns (“realized semivariances”), and high frequency data for the S&P 500 index and 105 individual stocks, this paper sheds new light on the predictability of equity price volatility. We show that future volatility is much more strongly related to the volatility of past negative returns than to that of positive returns, and this effect is stronger than that implied by standard asymmetric GARCH models. We also find that the impact of a jump on future volatility critically depends on the sign of the jump, with negative (positive) jumps in prices leading to significantly higher (lower) future volatility. A simple model exploiting these findings leads to significantly better out-of-sample forecast performance, across forecast horizons ranging from 1 day to 3 months”

Full article (PDF): Link

 
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Posted in Realized volatility

 

Buying VIX Calls As A Portfolio Hedge

25 May 2012

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

 
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Posted in Implied volatility

 
 
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