“Listed futures on VIX and its cousins give exposure to implied variance. But getting exposure to realised variance is very different and usually has been the realm of OTC variance swaps. Here we examine strategies to trade the realised variance using only listed instruments, with simple time-independent formulas not requiring models such as Black-Scholes.”

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“Asset prices are much more volatile during exchange trading hours than during non-trading hours. This paper considers three explanations for this phenomenon: (1) volatility is caused by public information which is more likely to arrive during normal business hours; (2) volatility is caused by private information which affects prices when informed investors trade; and (3) volatility is caused by pricing errors that occur during trading. Although a significant fraction of the daily variance is caused by mispricing, the behavior of returns around exchange holidays suggests that private information is the principle factor behind high trading-time variances.”

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“A study by Szado and Schneeweis found that a long protective collar strategy using six month put purchases and consecutive one month call writes earned far superior returns compared to a simple buy-and-hold strategy while reducing risk by almost 65%. The research evaluated more than ten years of data on the PowerShares QQQ exchange-traded fund (Ticker: QQQQ) and its associated options. The authors also extended the analysis to a more active implementation of the strategy. While the passive collar used a constant set of fixed rules, the active collar uses rules that adapt the collar to changing macroeconomic variables and market conditions. The active collar implementation generated higher returns than the passive implementation, while volatility was only slightly higher. Over the 122 month study period, the passive collar returned almost 150%, while the QQQ lost one-third of its value. The active collar outperformed both strategies and returned more than 200%. Finally, the study collared a small cap mutual fund. The return of the active mutual fund collar was four times the return of the fund, while the standard deviation was about one-third lower.”

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This is a presentation on volatility, tail hedging, and alternative investments given at the Asian Insurance Forum.

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“Systematic call overwriting strategies are valuable tools in the investment toolbox. They can provide income, attractive risk adjusted returns and the potential for a cushion during market downturns. In this paper, we explore call overwriting, the impact of strategy construction and performance across various market environments.”

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“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 [4] methodology; and variance swaps from vanilla options by the standard log-contract methodology.”

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“Trading in derivatives has caused investors, and especially market makers, to be concerned with the volatility of asset returns along with their direction. Uncertain and time-varying volatility imparts risk to an otherwise hedged position, and volatility risk is not easy to manage with ordinary instruments. Volatility swaps are a new class of derivative, for which an asset’s volatility itself is the underlying. This article describes how volatility swaps work, and derives pricing and hedging equations for them. Interestingly, the natural derivative instrument in this family would be based on variance, rather than volatility, since a variance swap can be replicated (pretty well) by a static portfolio of ordinary European calls and puts on the price of the underlying asset. The authors also show how to set up a volatility hedge when the available traded options exhibit a smile or skew pattern.”

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“Volatility swaps are forward contracts on future realized stock volatility. Variance swaps are similar contracts on variance, the square of future volatility. Both of these instruments provide an easy way for investors to gain exposure to the future level of volatility.

“Unlike a stock option, whose volatility exposure is contaminated by its stock-price dependence, these swaps provide pure exposure to volatility alone. You can use these instruments to speculate on future volatility levels, to trade the spread between realized and implied volatility, or to hedge the volatility exposure of other positions or businesses.

“In this report we explain the properties and the theory of both variance and volatility swaps, first from an intuitive point of view and then more rigorously. The theory of variance swaps is more straightforward. We show how a variance swap can be theoretically replicated by a hedged portfolio of standard options with suitably chosen strikes, as long as stock prices evolve without jumps. The fair value of the variance swap is the cost of the replicating portfolio. We derive analytic formulas for theoretical fair value in the presence of realistic volatility skews. These formulas can be used to estimate swap values quickly as the skew changes.

“We then examine the modifications to these theoretical results when reality intrudes, for example when some necessary strikes are unavailable, or when stock prices undergo jumps. Finally, we briefly return to volatility swaps, and show that they can be replicated by dynamically trading the more straightforward variance swap. As a result, the value of the volatility swap depends on the volatility of volatility itself.”

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“Volatility has always been considered a key measure within the field of finance. Financial markets have changed significantly over the last century and the recent financial crises have reshaped the markets in such a way that the role of volatility has become even more pronounced than it was before. The concept finds its use within important areas such as risk management, valuation and asset pricing in general, trading and many more.

“Increased market complexity have historically spurred the demand for more exotic derivatives for directional trading and hedging. In the 1990s a new asset class arose which provided the investor with the opportunity to take a direct position, not in the underlying itself, but in its volatility. With this new derivative class, volatility is no longer viewed as side product inherent in other derivatives, but as an independent asset class of its own. Variance and volatility swaps were the first and most fundamental products to be introduced in this asset class and ever since their introduction, the market for them has exploded. The products are in nature forward contracts which at maturity exchange the difference between a fixed strike and realized variance/volatility, scaled by a predetermined notional. Both are traded OTC which makes it difficult to assess the true market size but recent estimates indicate daily trading volumes of more than $35 million notional. Both market and academic interest for these products has increased in line with demand and much research has recently been devoted to develop efficient pricing methods.”

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“The Volatility Exchange™ (VolX®) plans to launch futures and options contracts based upon the realized volatility of U.S. equity indices. The futures version is named VolContract™ futures (VCs), which settle to the VolX indices known generically as RVOL™. The concept is both similar and dissimilar to the popular VIX® index and products marketed by the CBOE®. The two versions are similar in the notion that both VolX and CBOE are trying to provide volatility products to the marketplace. They are dissimilar because the VIX index and consequently VIX futures are based on implied volatility (the relative cost of options) while the RVOL index and consequently VCs are based on realized volatility (the actual, historical movement of the underlying index). VolContract futures are exchange‐tradable instruments that function similarly to a forward‐starting over‐the-counter volatility swap. They are expected to be launched on U.S. equity indices in 2013 and will come in two varieties: a 1‐month calculation period of realized volatility (1Vol™) and a 3‐month calculation period of realized volatility (3Vol™). For a detailed description of how these new instruments work, please visit the web site of The Volatility Exchange at www.volx.us. The goal of this paper is to demonstrate how a VC overlay can enhance the return and/or reduce the standard deviation of an equity portfolio. We chose the S&P 500 Total Return Index on the assumption that VolX will roll out products based upon this index.”

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