Volatility as an Asset Class: European Evidence

Abstract

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.     

Speculators,commodities and cross-market linkages

We use a unique, non-public dataset of trader positions in 17 U.S. commodity futures markets to provide novel evidence on those markets' financialization in the past decade. We then show that the correlation between the rates of return on investible commodity and equity indices rises amid greater participation by speculators generally, hedge funds especially, and hedge funds that hold positions in both equity and commodity futures markets in particular. We find no such relationship for commodity swap dealers, including index traders (CITs). The predictive power of hedge fund positions is weaker in periods of generalized financial market stress. Our results support the notion that who trades helps predict the joint distribution of commodity and equity returns. We find qualitatively similar but statistically weaker results using a proxy for hedge fund activity based on publicly available data.     

中国利率市场的价格发现——对国债现货、期货以及利率互换市场的研究

本文采用信息份额模型和基于向量自回归(VAR)模型的格兰杰因果检验,研究了国债现货、国债期货和利率互换三个市场之间的价格发现机制。信息份额模型表明,从整体来看利率互换相对于国债期货和国债现货都具有信息优势,而国债期货相对于国债现货具有信息优势。另外,国债期货的价格发现能力相对于另外两个市场都在随时间增强。格兰杰因果检验结果显示,利率互换在价格发现中单向引领国债期货以及国债现货,国债期货单向引领国债现货。所有结果一致表明, 利率互换和国债期货这两种利率衍生产品在引导中国利率市场价格发现中发挥了重要作用。     

Investor structure and the informational efficiency of commodity futures prices

This article investigates the impact of the trading positions of hedgers (i.e., producers, merchants, processors, or users of a commodity), speculators (i.e., commodity pool operators, trading advisors, or hedge funds), and swap dealers on the price formation process in the agricultural, metal, and energy futures markets. The hedgers' relative positions exert negative impacts on price efficiency in commodity futures markets. Hedgers are less likely to be information motivated, so their trading delays the price formation process. However, speculators' positions have positive impacts on price efficiency because speculators correct pricing errors. This study also offers evidence that the role of swap dealers, similar to speculators in futures markets, is to provide liquidity and cross-market arbitrage. These findings highlight the role of producers, hedge funds, and swap dealers in price formation processes in commodity futures—information that is beneficial to academics, practitioners, and regulators.     

The Default Risk of Swaps

We characterize the exchange of financial claims from risky swaps. These transfers are among three groups: shareholders, debtholders, and the swap counterparty. From this analysis we derive equilibrium swap rates and relate them to debt market spreads. We then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders. In a simplified case, we obtain closed-form solutions for the value of the default risk in the swap. For interest-rate swaps, we obtain numerical solutions for the equilibrium swap rate, including default risk. We compare these with equilibrium debt market default risk spreads.     

Financialization and speculators risk premia in commodity futures markets

J.M. Keynes coined the term normal backwardation, a situation where a futures price for a particular expiry month is less than the expected spot price for that month. He argued hedgers pay speculators a risk premium, giving rise to normal backwardation. We study the behavior of commodity futures before and since financialization of the markets, which started about 20 years ago. We find the poor returns to managed futures in recent years are likely due to the impact of financialization and the associated outside money suppressing the futures risk premium.     

The dynamics of sovereign yields over swap rates in the Eurozone market

We explore the dynamics of the adjusted swap spread (calculated as the difference between the swap rate and sovereign yields over the credit default swap premium) in the Eurozone market by studying three markets simultaneously: 1) sovereign bonds, 2) credit default swaps (CDS), and 3) swap rates. We find a strong relationship between the markets. Specifically, based on the no-arbitrage argument, we show that the difference between the Euribor and Repo rates is a key driver of the adjusted swap spread. However, illiquidity premiums and systemic risk also play an essential role in times of economic stress and for less creditworthy countries. The findings also shed light on the recent negative swap spreads puzzle in the United States.     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Variance risk premiums in foreign exchange markets

Based on the theory of static replication of variance swaps we assess the sign and magnitude of variance risk premiums in foreign exchange markets. We find significantly negative risk premiums when realized variance is computed from intraday data with low frequency. As a likely consequence of microstructure effects however, the evidence is ambiguous when realized variance is based on high-frequency data. Common to all estimates, variance risk premiums are highly time-varying and inversely related to the risk-neutral expectation of future variance.When we test whether variance risk premiums can be attributed to classic risk factors or fear of jump risk, we find that conditional premiums remain significantly negative. However, we observe a strong relationship between the size of log variance risk premiums and the VIX, the TED spread and the general shape of the implied volatility function of the corresponding currency pair. Overall, we conclude that there is a separately priced variance risk factor which commands a highly time-varying premium.     

Modeling volatility and changes in the swap spread

We investigate the determinants of changes in U.S. interest rate swap spreads using a model that explicitly allows for volatility interactions between swaps of different terms to maturity. Changes in the swap spread are found to be positively related to interest rate volatility, to changes in the default risk premium in the corporate bond market, and to changes in the liquidity premium for government securities. Swap spread changes are negatively related to changes in the level of interest rates and changes in the slope of the term structure. We also find that there is a strong and significant volatility interaction among spreads for swaps of different maturities and that the process for the conditional variance of the spread is highly persistent across all maturities.     

商品期货投资收益问题研究

按照持有期货合约的部位,将商品期货交易者细分为：标的商品生产商、加工商和投机者。在满足终期效用最大化的条件下,通过联立商品期货、现货和证券市场,推导出一个商品期货投资收益模型,证明了商品期货投资收益由期货市场的系统性风险溢价和非系统性风险溢价两部分组成,并解释了“持有期成本套利”、“现货一期货溢价”和“资本资产定价”三种理论适用于确定商品期货投资收益的前提条件。根据国内商品期货市场与证券市场之间存在负相关性的实证结论,说明发展商品基金、减少证券一商品期货市场跨市场投资的交易成本等措施有利于我国资本市场的发展和完善。     

What does futures market interest tell us about the macroeconomy and asset prices?

Economists have traditionally viewed futures prices as fully informative about future economic activity and asset prices. We argue that open interest could be more informative than futures prices in the presence of hedging demand and limited risk absorption capacity in futures markets. We find that movements in open interest are highly pro-cyclical, correlated with both macroeconomic activity and movements in asset prices. Movements in commodity market interest predict commodity returns, bond returns, and movements in the short rate even after controlling for other known predictors. To a lesser degree, movements in open interest predict returns in currency, bond, and stock markets.     

A Model of Financialization of Commodities

We analyze how institutional investors entering commodity futures markets, referred to as the financialization of commodities, affect commodity prices. Institutional investors care about their performance relative to a commodity index. We find that all commodity futures prices, volatilities, and correlations go up with financialization, but more so for index futures than for nonindex futures. The equity‐commodity correlations also increase. We demonstrate how financial markets transmit shocks not only to futures prices but also to commodity spot prices and inventories. Spot prices go up with financialization, and shocks to any index commodity spill over to all storable commodity prices.     

Predictability of structural co-movement in commodity prices: the role of technical indicators

This paper investigates the financialization and structural co-movement of several commodity futures using factor variance decomposition and predictability of technical indicators and macro variables. We find that financialization is still a dominant player in the commodity market and that recent commodity price fluctuations can be significantly and robustly forecasted by technical analyses of commodity index investments. Moreover, the co-movement of commodities is demonstrated by variance decomposition and explained as commodity index investment, which provides evidence of financialization. The overall empirical analysis reveals that technical indicators and macro variables can statistically and economically forecast the indexed investment and off-index trading, respectively, which indicates that they are suitable predictors of the commodity markets.     

Arithmetic variance swaps

Biases in standard variance swap rates (VSRs) can induce substantial deviations below market rates. Defining realized variance as the sum of squared price (not log-price) changes yields an ‘arithmetic’ variance swap with no such biases. Its fair value has advantages over the standard VSR: no discrete monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair value for the arithmetic variance swap and compare it with the standard VSR by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher moment arithmetic swap.     

The Impact of Collateralization on Swap Rates

Interest rate swap pricing theory traditionally views swaps as a portfolio of forward contracts with net swap payments discounted at LIBOR rates. In practice, the use of marking‐to‐market and collateralization questions this view as they introduce intermediate cash flows and alter credit characteristics. We provide a swap valuation theory under marking‐to‐market and costly collateral and examine the theory's empirical implications. We find evidence consistent with costly collateral using two different approaches; the first uses single‐factor models and Eurodollar futures prices, and the second uses a formal term structure model and Treasury/swap data.     

Moment swaps

In this paper we discuss moment swaps. These derivatives depend on the realized higher moments of the underlying. A special case is the nowadays popular variance swaps. After introducing moment swaps we discuss how to hedge these derivatives. Moreover, we show how the classical hedge of the variance swap in terms of a position in log-contracts and a dynamic trading strategy can be significantly enhanced by using third moment swaps.     

Can the choice of interpolation method explain the difference between swap prices and futures prices?

The standard model linking the swap rate to the rates in a contemporaneous strip of futures interest rate contracts typically produces biased estimates of the swap rate. Institutional differences usually require some form of interpolation to be employed and may in principle explain this empirical result. Using Australian data, we find evidence consistent with this explanation and show that model performance is greatly improved if an alternative interpolation method is used. In doing so, we also provide the first published Australian evidence on the accuracy of the futures‐based approach to pricing interest rate swaps.     

Regulatory reform and market efficiency: The case of Indian agricultural commodity futures markets

We present the results of two efficiency measures that include intraday return predictability measure based on order imbalance and measures of several variance ratio tests on intraday subsamples of nine major Indian agricultural commodity futures (castor seed, cotton oil cake, rape mustard seed, soybean, refined soya oil, crude palm oil, jeera, chana, and turmeric) quoted in the National Commodity and Derivatives Exchange (NCDEX). We perform the efficiency measures on five subsamples with holding periods of 5, 10, 15, 30, and 60 min over two sample periods following the announcement of the merger between the Forward Market Commission (FMC) and Securities Exchange Board of India (SEBI). We compare results of tests of weak-form market efficiency of futures markets between two periods (pre-merger period and post-merger period). Our results confirm that Indian agricultural commodity futures markets continue to remain inefficient in the short-term during both pre-merger and post-merger periods. Based on these findings, it is likely that profitable trading strategies in the short intraday intervals will be available for traders and market participants during post-merger period. Thus, regulators must focus more on policy initiative so as to enhance market quality in order to address such inefficiencies in Indian commodity futures markets.     

Does economic policy uncertainty drive nonlinear risk spillover in the commodity futures market?

We propose the rolling tail-event driven network technique (RTENET) to measure the dynamic nonlinear tail risk spillover of 20 US commodity futures. In addition, we investigate the effect of economic policy uncertainty (EPU) on risk spillover based on quantile-on-quantile regression (QQR). We find that the risk spillover effect increases sharply and that the market is tightly connected when EPU is at a high level. Crude oil, silver and corn, the three greatest risk transmitters in the system, need more attention. More importantly, the effect of EPU on the risk spillover of the commodity futures market is asymmetric and heterogeneous. When the risk spillover falls within extremely high quantiles, a significant positive effect of EPU is observed. In addition, grain and soft crops are more sensitive to EPU. Our findings provide a reference for policy-makers and investors to manage commodity futures markets in different uncertainty periods.