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Archive for the ‘Realized volatility’ Category

Realized Volatility and Variance: Options via Swaps

14 Feb

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

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

 

Volatility Arbitrage Indices – A Primer

12 Jan

Article by: Keith Loggie
Published by: Standard & Poor’s
Date: Jul 2008

“In broad terms, volatility arbitrage can be used to describe trading strategies based on the
difference in volatility between related assets, for instance the implied volatility of two
options based on the same underlying asset. However, the term is most commonly used
to describe strategies that take advantage of the difference between the forecasted future
volatility of an asset and the implied volatility of options based on that asset. This
strategy is often implemented through a delta neutral portfolio consisting of an option and
its underlying asset. The return on such a portfolio will be based not on the future returns
of the underlying asset but rather on the volatility of its future price movements. Buying
an option and selling the underlying results in a long volatility position, while selling an
option and buying the underlying results in a short volatility position. A long volatility
position will be profitable to the extent that the realized volatility on the underlying is
ultimately higher than the implied volatility on the option at the time of the trade.”

Full article (PDF): Link

 
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Posted in Implied volatility, Realized volatility, Trading ideas

 

The predictive power of implied volatility: Evidence from 35 futures markets

21 Dec

Article by: Andrew Szakmary, Evren Ors, Jin Kyoung Kim, Wallace N. Davidson III
Published by: Elsevier, Journal of Banking and Finance
Date: 19 Apr 2002

“Using data from 35 futures options markets from eight separate exchanges, we test how well the implied volatilities (IVs) embedded in option prices predict subsequently realized volatility (RV) in the underlying futures. We find that for this broad array of futures options, IV performs well in a relative sense. For a large majority of the commodities studied, the implieds outperform historical volatility (HV) as a predictor of the subsequently RV in the underlying futures prices over the remaining life of the option. Indeed, in most markets examined, regardless of whether it is modeled as a simple moving average or in a GARCH framework, HV contains no economically significant predictive information beyond what is already incorporated in IV. These findings add to previous research that has focused on currency and crude oil futures by extending the analysis into a very broad array of contracts and exchanges. Our results are consistent with the hypothesis that futures options markets in general, with their minimal trading frictions, are efficient.”

Full article (PDF): Link

 
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Posted in Implied volatility, Realized volatility

 
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