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Archive for June, 2012

Analysis of Carr and Lee’s Quadratic Variation Derivatives Framework

29 Jun

Article by: Peter Larkin
Published by: Kellogg College, University of Oxford
Date: 18 Apr 2012

“Over the last years, there has been a growing interest in pricing and hedging financial products contingent on the volatility or variance of tradable assets. In parallel to this, there is a fundamental need to price in such a way as to capture all the information available in the market – in particular, in the observed implied volatility smile.

“The volatility of an equity is the simplest measure of how risky it is, or perhaps how much it is likely to move around in the future, based on how it has moved historically, or what the market implies it to be in the future. Investors may wish to trade volatility if they believe they have some insight into the level of future volatility. For example, if a trader thinks that volatility is currently too low, he or she may want to take a position which allows them to profit if volatility increases.

“In this work we are interested in a one important part of this growing area – the pricing and hedging or European options whose pay-off at maturity depends on the quadratic variation of the underlying process.”

Full article (PDF): Link

 
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Posted in Realized volatility

 

Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits

27 Jun

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

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