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The Journal of Derivatives

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Primary Article

A Tale of Two Indices

Peter Carr and Liuren Wu
The Journal of Derivatives Spring 2006, 13 (3) 13-29; DOI: https://doi.org/10.3905/jod.2006.616865
Peter Carr
The director of the Quantitative Finance Research group at Bloomberg LP and the director of the Masters in Mathematical Finance program at the Courant Institute of New York University, NY.
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  • For correspondence: pcarr4@bloomberg.com
Liuren Wu
An associate professor of economics and finance at the Zicklin School of Business, Baruch College, City University of New York, NY.
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  • For correspondence: liuren_wu@baruch.cuny.edu
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Abstract

Pricing options involves a volatility input. Since volatility is not directly observable and it also varies stochastically over time, volatility risk is a significant concern for most option traders. Not surprisingly, then, there has always been considerable interest in the CBOE's VIX volatility index, although relatively little trading of derivatives based on it. The original VIX was a weighted average of Black-Scholes implied volatilities, which made it (in principle) a good estimator of future volatility, but hard to replicate with traded securities. The original VIX has been recently replaced by a new formula that is not model dependent. In this article, Carr and Wu review the old VIX (now called the VXO) and the new VIX and present a wide variety of results on their behavior. An interesting difference is that the new VIX, squared, is a good hedge for realized variance. This makes the new VIX a better underlier for volatility derivative contracts, which are now being launched into the marketplace by the CBOE. The article examines the performance of the two indices as forecasts of realized volatility, and shows how the VIX responds around an uncertainty diminishing information event, meetings of the Federal Open Market Committee. Carr and Wu also obtain interesting results on the market's volatility risk premium from direct measurement of risk neutral volatility in the VIX.

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The Journal of Derivatives
Vol. 13, Issue 3
Spring 2006
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A Tale of Two Indices
Peter Carr, Liuren Wu
The Journal of Derivatives Feb 2006, 13 (3) 13-29; DOI: 10.3905/jod.2006.616865

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A Tale of Two Indices
Peter Carr, Liuren Wu
The Journal of Derivatives Feb 2006, 13 (3) 13-29; DOI: 10.3905/jod.2006.616865
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  • Do Properly Anticipated Prices Fluctuate Randomly? Evidence from VIX Futures Markets
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  • VIX Futures Pricing with Affine Jump-GARCH Dynamics and Variance-Dependent Pricing Kernels
  • Pricing Bermudan Variance Swaptions Using Multinomial Trees
  • Model-Based versus Model-Free Implied Volatility: Evidence from North American, European, and Asian Index Option Markets
  • An Asset Class Characterization of the U.S. Equity Index Volatility Risk Premium
  • The Implied Convexity of VIX Futures
  • The Efficiency of the VIX Futures Market: * A Panel Data Approach
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