Common risk factors in the U.S. and UK interest rate swap markets: Evidence from a nonlinear vector autoregression approach

This paper produces evidence in support of the existence of common risk factors in the U.S. and UK interest rate swap markets. Using a multivariate smooth transition autoregression (STVAR) framework, we show that the dynamics of the U.S. and UK swap spreads are best described by a regime‐switching model. We identify the existence of two distinct regimes in U.S. and UK swap spreads; one is characterized by a “flat” term structure of U.S. interest rates and the other is characterized by an “upward” sloping U.S. term structure. In addition, we show that there exist significant asymmetries on the impact of the common risk factors on the U.S. and UK swap spreads. Shocks to UK oriented risk factors have a strong effect on the U.S. swap markets during the “flat” slope regime but a very limited effect otherwise. On the other hand, U.S. risk factors have a significant impact on the UK swap markets in both regimes. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:221–250, 2004     

Identifying the Factors that Affect Interest‐Rate Swap Spreads: Some Evidence from the United States and the United Kingdom

We assess the ability of the factors proposed in previous research to account for the stochastic evolution of the term structure of the U.S. and U.K. swap spreads. Using as factor proxies the level, volatility, and slope of the zero‐coupon government yield curve as well as the Treasury‐bill—London Interbank Offer Rate (LIBOR) spread and the corporate bond spread, we identify a procyclical behavior for the short‐maturity U.S. swap spreads and a countercyclical behavior for longer maturity U.S. swap spreads. Liquidity and corporate bond spreads are also significant, but their importance varies with maturity. The liquidity premium is more important for short‐maturity swap spreads, although the corporate bond spread affects long‐maturity swap spreads. For the United Kingdom, swap spreads are countercyclical across maturities. In addition, we find that shocks to the liquidity premium are more significant for long‐maturity swaps and that the links between corporate bond markets and swap markets are much stronger than in the United States. When we look at the links between U.S. and U.K. swap markets, we identify a significant influence of the U.S. factors on the U.K. swap spreads across maturities. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:737–768, 2001     

Pricing models of equity swaps

This article provides a generalized formula for pricing equity swaps with constant notional principal when the underlying equity markets and settlement currency can be set arbitrarily. To derive swap values using the risk‐neutral valuation method, the swap payment is replicated at each settlement date by constructing a self‐financing portfolio. To obtain the foreign equity index return denominated in the domestic or in a third currency, equity‐linked foreign exchange options are used to hedge the exchange rate risk. It is found that if the swap involves international equity markets, then the swap value contains an extra term which reflects the currency hedging costs. This methodology can easily be applied to price various types of equity swaps simply by modifying the specifications of the model presented here as required. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:751–772, 2003     

Dissecting interbank risk using basis swap spreads

This paper analyses interbank risk using the information content of basis swap (BS) spreads, floating-to-floating interest rate swaps whose payments are associated with euro deposit rates for alternative tenors. To identify the impact of shocks affecting interbank risk, we propose an empirical model that decomposes BS quotes into their expected and unexpected components. These unobservable constituents of BS spreads are estimated by solving a signal extraction problem using a particle filter. We find that expected components covariate with aggregate liquidity and risk aversion while systemic risk arises as the main driver behind unexpected fluctuations. Our empirical findings suggest that macroprudential analysis emerges as a key device to ease asset pricing in a new multi-curve scenario.     

Affine multiple yield curve models

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath–Jarrow–Morton modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded overnight indexed swap rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multicurve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed‐form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.     

A two‐mean reverting‐factor model of the term structure of interest rates

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference) between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor (Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities. However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data, and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003     

The compatibility of one‐factor market models in caps and swaptions markets: Evidence from their dynamic hedging performance

This study examines the dynamic hedging performance of the one‐factor LIBOR and swap market models in both caps and swaptions markets, using a procedure similar to the way that these models are used in practice. The effects of different calibration methods on model performance are investigated as well. The LIBOR market models and the swap market models are calibrated to the cross‐sectional Black implied volatilities for caps and swaptions respectively; the test is based on their effectiveness in hedging floors and swaptions that are not used in the calibration. We find that the LIBOR market models outperform the swap market models in hedging floors and perform as well as the swap market models in hedging swaptions. Our results also show that incorporating a humped volatility structure into these models does not significantly improve their hedging performance. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:109–130, 2008     

Spot‐futures spread,time‐varying correlation,and hedging with currency futures

This article investigates the effects of the spot‐futures spread on the return and risk structure in currency markets. With the use of a bivariate dynamic conditional correlation GARCH framework, evidence is found of asymmetric effects of positive and negative spreads on the return and the risk structure of spot and futures markets. The implications of the asymmetric effects on futures hedging are examined, and the performance of hedging strategies generated from a model incorporating asymmetric effects is compared with several alternative models. The in‐sample comparison results indicate that the asymmetric effect model provides the best hedging strategy for all currency markets examined, except for the Canadian dollar. Out‐of‐sample comparisons suggest that the asymmetric effect model provides the best strategy for the Australian dollar, the British pound, the deutsche mark, and the Swiss franc markets, and the symmetric effect model provides a better strategy than the asymmetric effect model in the Canadian dollar and the Japanese yen. The worst performance is given by the naïve hedging strategy for both in‐sample and out‐of‐sample comparisons in all currency markets examined. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1019–1038, 2006     

An Analytic Solution for Interest Rate Swap Spreads

This paper argues that liquidity differences between government securities and short–term Eurodollar borrowings account for interest rate swap spreads. It then models the convenience of liquidity as a linear function of two mean–reverting state variables and values it. The interest rate swap spread for a swap of particular maturity is the annuitized equivalent of this value. It has a closed form solution: a simple integral. Special cases examined include the Vasicek and Cox–Ingersoll–Ross one–factor term structure models. Numerical values for the parameters in both special cases illustrate that many realistic ‘swap spread term structures’ can be replicated. Model parameters are estimated using weekly data on the term structure of swap spreads from several countries. The model fits the data well.     

Time‐varying market price of risk in the crude oil futures market

In this study, a three‐factor model of crude oil prices is estimated, which incorporates a time‐varying market price of risk. The model is able to accurately capture the term structure of futures prices with evidence suggesting that risk premiums in the crude oil market are time‐varying. Using the cross‐section of futures prices, we estimate a time‐series of the market price of risk in the crude oil market implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:779–807, 2011     

The Co‐Movement of Credit Default Swap Spreads,Equity Returns and Volatility: Evidence from Asia‐Pacific Markets

We provide a comprehensive analysis of the co‐movement of credit default swap (CDS), equity, and volatility markets in four Asia‐Pacific countries at firm and index level during the period 2007–2010. First, we examine lead–lag relationships between CDS spread changes, equity returns, and changes in volatility using a vector autoregressive model. At the firm level equity returns lead changes in CDS spreads and realized volatility. However, at the index level the intertemporal linkages between the three markets are less clear‐cut. Second, we apply the measures proposed by Diebold and Yilmaz (2014) to an analysis of volatility spillovers among the CDS, equities, and volatility asset classes. The results suggest that realized volatility (at firm level) and implied volatility (at index level) are the main transmitters of cross‐market volatility spillovers. Third, we analyze the impact of various structural factors and confirm the importance of realized volatility of equity returns as a determinant of CDS spreads.     

Determinants of Japanese Yen interest rate swap spreads: Evidence from a smooth transition vector autoregressive model

This study investigates the determinants of variations in the yield spreads between Japanese yen interest rate swaps and Japan government bonds for a period from 1997 to 2005. A smooth transition vector autoregressive (STVAR) model and generalized impulse response functions are used to analyze the impact of various economic shocks on swap spreads. The volatility based on a GARCH (generalized autoregressive conditional heteroskedasticity) model of the government bond rate is identified as the transition variable that controls the smooth transition from a high volatility regime to a low volatility regime. The break point of the regime shift occurs around the end of the Japanese banking crisis. The impact of economic shocks on swap spreads varies across the maturity of swap spreads as well as regimes. Overall, swap spreads are more responsive to the economic shocks in the high volatility regime. Moreover, a volatility shock has profound effects on shorter maturity spreads, whereas the term structure shock plays an important role in impacting longer maturity spreads. Results of this study also show noticeable differences between the nonlinear and linear impulse response functions. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:82–107, 2008     

Futures hedging when the structure of the underlying asset changes: The case of the BIFFEX contract

This article is concerned with the hedging effectiveness of futures contracts whose underlying asset is an index, when the structure of this index is changing. The case of the freight futures (BIFFEX) contract is examined here. Investigation of this issue is particularly interesting as the composition of its underlying asset, the Baltic Freight Index (BFI), has been revised on a number of occasions in order to improve the hedging performance of the market; previous empirical evidence on the market indicates substantially lower variance reduction (4–19%), compared to other markets (up to 98%). The BFI is a weighted average dry‐cargo freight rate index, compiled from actual freight rates on 11 shipping routes that are dissimilar in terms of vessel sizes and transported commodities. The hedging effectiveness of the market is investigated using both constant and time‐varying hedge ratios, estimated through bivariate error correction GARCH models. Our results indicate that the effectiveness of the BIFFEX contract as a centre for risk management has strengthened over the recent years as a result of the more homogeneous composition of the index. This by itself indicates that the latest restructuring of the index, in November 1999, which is aimed at increasing its homogeneity even further, is likely to have a beneficial impact on the market. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:775–801, 2000     

The Relation between Physical and Risk‐neutral Cumulants

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. The empirical observation on skewness research suggests that derivative professionals may also desire to hedge beyond volatility risk and there exists the need to hedge higher‐moment market risks, such as skewness and kurtosis risks. We study two derivative contracts – skewness swap and kurtosis swap – which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the both skewness and kurtosis risk premiums are significantly negative.     

Looking for contagion in currency futures markets

This article tests whether there are pure contagion effects in both conditional means and volatilities among British pound, Canadian dollar, Deutsche mark, and Swiss franc futures markets during the 1992 ERM crisis. A conditional version of international capital asset pricing model (ICAPM) in the absence of purchasing power parity (PPP) is used to control for economic fundamentals. The empirical results indicate that overall there are no mean spillovers among those futures markets, but they are detected during the crisis period. That is, past return shocks originating in any one of the four markets have no impact on the other three markets during the entire sample period, suggesting that these markets are weak‐form efficient. However, this weak‐form market efficiency fails to hold during the market turmoil, especially for British pound and Swiss franc, and the sources of contagion‐in‐mean effects are mainly due to the return shocks originating in three European currency futures markets. As for the contagion‐in‐volatility, it is detected for British pound only because its conditional volatility is influenced by the negative volatility shocks from Canadian dollar, Deutsche mark, and Swiss franc, with Deutsche mark playing the dominant role in generating these shocks. JEL Classifications: C32; F31; G12. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:957–988, 2003     

Volatilities in emerging MENA stock markets

This article examines the interrelationships among the emerging stock markets of the Middle East and North Africa (MENA) region, as well as the relationship between each MENA stock market and the larger and more developed markets of Europe and the United States. It explores whether MENA stock markets can offer international investors unique risk/return characteristics to diversify international and regional portfolios. This study adds to the existing literature by focusing—for the first time— on the dynamic relationships in the volatilities of the returns in MENA stock markets. The econometric part of the article uses the causality‐in‐variances GARCH model, the TARCH and ARCH‐M models, and VAR analysis to model conditional volatilities in stock market returns and the dynamic responses of volatilities to innovations in conditional variances. © 2006 Wiley Periodicals, Inc.     

Benchmark tipping and the role of the swap market in price discovery

The author uses a high‐frequency data set to investigate the roles of the sterling swap and futures markets in price discovery at the short‐end of the sterling yield curve. Information flows between the futures and swap markets are found to be largely contemporaneous. Causal information flows are bidirectional, although the futures market dominates the information flow over the very short term. Thus, the futures market remains the primary locus of price discovery despite the increased use of swaps as a pricing benchmark and hedging instrument in recent years. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:981–1001, 2007     

Intraday price formation and bid–ask spread components: A new approach using a cross‐market model

This study examines the intraday formation process of transaction prices and bid–ask spreads in the KOSPI 200 futures market. By extending the structural model of Madhavan, A., Richardson, M., and Roomans, M. ( 1997 ), we develop a unique cross‐market model that can decompose spread components and explain intraday price formation for the futures market by using the order flow information from the KOSPI 200 options market, which is a market that is closely related to the futures market as well as considered to be one of the most remarkable options markets in the world. The empirical results indicate that the model‐implied spread and the permanent component of the spread that results from informed trading tend to be underestimated without the inclusion of options market information. Further, the results imply that trades of in‐the‐money options, which have high delta values, generally incur a more adverse information cost component (the permanent spread component) of the futures market than those of out‐of‐the‐money options, which have relatively low delta values. Finally, we find that the adverse information cost component that is estimated from the cross‐market model exhibits a nearly U‐shaped intraday pattern; however, it sharply decreases at the end of the trading day. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

Variance risk premiums and predictive power of alternative forward variances in the corn market

We propose a fear index for corn using the variance swap rate synthesized from out‐of‐the‐money call and put options as a measure of implied variance. We find negative and time‐varying variance risk premiums (realized variance minus implied variance) in the corn market from 1987 to 2009. Our results contrast with Egelkraut, Garcia, and Sherrick (2007), but are in line with the findings of Simon (2002). We conclude that our synthesized model‐free implied variance estimation procedure contains superior information about future realized variance relative to traditional model‐dependent estimating procedures: the implied variance model by Black (1976) and the seasonal GARCH(1, 1) forecasted variance model. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:587–608, 2012