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Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts

01 Mar 2011

Article by: Torben G. Andersen, Tim Bollerslev
Published by: International Economic Review
Date: 4 Nov 1998

“A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, the authors show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex post interdaily volatility measurements based on high-frequency intradaily data are also discussed. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.”

Full article (requires subscription): Link

 
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Posted in Trading ideas

 

Robust Replication of Volatility Derivatives

15 Feb 2011

Article by: Peter Carr and Roger Lee
Published by: University of Chicago
Date: 31 May 2009

“In a nonparametric setting, we develop trading strategies to replicate volatility derivatives
— contracts which pay functions of the realized variance of an underlying asset’s returns. The
replicating portfolios trade the underlying asset and vanilla options, in quantities that we express in terms of vanilla option prices, not in terms of parameters of any particular model. Likewise, we find nonparametric formulas to price volatility derivatives, including volatility swaps and variance options. Our results are exactly valid, if volatility satisfies an independence condition. In case that condition does not hold, our formulas are moreover immunized, to first order, against nonzero correlation.”

Full article (PDF): Link

 
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Posted in Realized volatility, Trading ideas

 

Realized Volatility and Variance: Options via Swaps

14 Feb 2011

Article by: Peter Carr and Roger Lee
Published by: University of Chicago
Date: 26 Oct 2007

“In this paper we develop strategies for pricing and hedging options on realized variance and
volatility. Our strategies have the following features.

  • Readily available inputs: We can use vanilla options as pricing benchmarks and as hedging
    instruments. If variance or volatility swaps are available, then we use them as well. We do
    not need other inputs (such as parameters of the instantaneous volatility dynamics).
  • Comprehensive and readily computable outputs: We derive explicit and readily computable
    formulas for prices and hedge ratios for variance and volatility options, applicable at all times
    in the term of the option (not just inception).
  • Accuracy and robustness: We test our pricing and hedging strategies under skew-generating
    volatility dynamics. Our discrete hedging simulations at a one-year horizon show mean absolute
    hedging errors under 10%, and in some cases under 5%.
  • Easy modification to price and hedge options on implied volatility (VIX).

 
“Specifically, we price and hedge realized variance and volatility options using variance and volatility
swaps. When necessary, we in turn synthesize volatility swaps from vanilla options by the Carr-Lee
methodology; and variance swaps from vanilla options by the standard log-contract methodology.”

Full article (PDF): Link

 
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Posted in Hedging, Realized volatility

 

Forecasting Volatility of S&P 500 Index

11 Feb 2011

Article by: Pawan Madhogarhia
Published by: The Pennsylvania State University

“Why are we interested to forecast the volatility of S&P 500, a proxy for the stock market? If
stock market volatility remained constant over time, forecasting volatility would have been
an easy task. If this were true, volatility measured through a measure such as standard
deviation in the current period could have been applied in the future. There are often wide
swings in the market followed by larger swings. This implies that volatility is not constant
over time and is often referred to as heteroscedasticity. Stock market volatility is important
for several reasons. Detection of volatility-trends would provide insight for designing
investment strategies and for portfolio management. The volatility of S&P 500 is important
to derive the price of an option on S&P 500 index for the remaining life of the option. The
stock market volatility forecast is also an important input for dynamic portfolio insurance
strategies.

“Forecasting stock market volatility would be useful for holders and writers of options on the
S&P 500 index. Gains on straddles or spreads depend on the volatility of underlying security.
The more volatile a security is, the larger the gain to the straddle-trader or the spread-trader.
The spread-trader and the straddle-trader are not concerned about the direction of change;
rather they are concerned about the fluctuations in prices.”

Full article (PDF): Link

 
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Posted in Investing ideas, Realized volatility

 
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