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54
Term structure dynamics in theory and reality
 Review of Financial Studies
, 2003
"... This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in ..."
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Cited by 101 (11 self)
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This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jumpdiffusion, or have “switching regimes. ” Then the goodnessoffits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixedincome derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1
Do Bonds Span the Fixed Income Markets? Theory and Evidence for ‘Unspanned’ Stochastic Volatility
 Journal of Finance
, 2002
"... Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to vola ..."
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Cited by 77 (1 self)
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Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to volatility risk. We term this empirical feature “unspanned stochastic volatility ” (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USVmodels, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.
Design and Estimation of Quadratic Term Structure Models
, 2001
"... We consider the design and estimation of quadratic term structure models. We start with a list of stylized facts on interest rates and interest rate derivatives, classified into three layers: (1) general statistical properties, (2) forecasting relations, and (3) conditional dynamics. We then investi ..."
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Cited by 27 (5 self)
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We consider the design and estimation of quadratic term structure models. We start with a list of stylized facts on interest rates and interest rate derivatives, classified into three layers: (1) general statistical properties, (2) forecasting relations, and (3) conditional dynamics. We then investigate the implications of each layer of property on model design and strive to establish a mapping between evidence and model structures. We calibrate a twofactor model that approximates these three layers of properties well, and illustrate how the model can be applied to pricing interest rate derivatives.
Unspanned stochastic volatility and the pricing of commodity derivatives
"... Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasianalytical prices of options on futures contracts, ..."
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Cited by 25 (2 self)
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Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasianalytical prices of options on futures contracts, and dynamics of the futures curve in terms of a lowdimensional affine state vector. We estimate the model on NYMEX crude oil derivatives using an extensive panel data set of 45,517 futures prices and 233,104 option prices, spanning 4082 business days. We find strong evidence for two, predominantly unspanned, volatility factors. JEL Classification: G13
Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities? Working Paper
, 2006
"... In fixed income markets, volatility is unspanned if volatility risk cannot be hedged with bonds. We first show that all affine term structure models with state space RM+ ×RN−M can be drift normalized and show when the standard variance normalization can be obtained. Using this normalization, we find ..."
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Cited by 20 (5 self)
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In fixed income markets, volatility is unspanned if volatility risk cannot be hedged with bonds. We first show that all affine term structure models with state space RM+ ×RN−M can be drift normalized and show when the standard variance normalization can be obtained. Using this normalization, we find conditions for a wide class of affine term structure models to exhibit unspanned stochastic volatility (USV). We show that the USV conditions restrict both the mean reversions of risk factors and the cross section of conditional yield volatilities. The restrictions imply that previously studied affine USV models are unlikely to be able to generate the observed cross section of yield volatilities. However, more general USV models can match the cross section of bond volatilities. 1.
A general stochastic volatility model for the pricing of interest rate derivatives
 Review of Financial Studies
, 2009
"... We develop a tractable and flexible stochastic volatility multifactor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasianalytical prices of zerocoupon bond options and dynamics of the forward rate curve, under both ..."
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Cited by 20 (3 self)
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We develop a tractable and flexible stochastic volatility multifactor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasianalytical prices of zerocoupon bond options and dynamics of the forward rate curve, under both the actual and riskneutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.
On the geometry of the term structure of interest rates
 Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
"... Abstract. We present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates. This includes an extension of the Frobenius theorem for Fréchet spaces in particular. This approach puts new light on many of the classical models, such as th ..."
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Cited by 19 (8 self)
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Abstract. We present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates. This includes an extension of the Frobenius theorem for Fréchet spaces in particular. This approach puts new light on many of the classical models, such as the HullWhite extended Vasicek and CoxIngersollRoss short rate models. The notion of a finite dimensional realization (FDR) is central for this analysis: we motivate it, classify all generic FDRs and provide some new results for the corresponding factor processes, such as hypoellipticity of its generators and the existence of smooth densities. Furthermore we include finite dimensional external factors, thus admitting a stochastic volatility structure. 1.
Design and Estimation of MultiCurrency Quadratic Models
 Review of Finance
"... Abstract. To simultaneously account for the properties of interestrate term structure and foreign exchange rates within one arbitragefree framework, we propose a class of multicurrency quadratic models (MCQM) with an (m + n) factor structure in the pricing kernel of each economy. The m factors mo ..."
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Cited by 18 (2 self)
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Abstract. To simultaneously account for the properties of interestrate term structure and foreign exchange rates within one arbitragefree framework, we propose a class of multicurrency quadratic models (MCQM) with an (m + n) factor structure in the pricing kernel of each economy. The m factors model the term structure of interest rates. The n factors capture the portion of the exchange rate movement that is independent of the term structure. Our modeling framework represents the first in the literature that not only explicitly allows independent currency movement, but also guarantees internal consistency across all economies without imposing any artificial constraints on the exchange rate dynamics. We estimate a series of multicurrency quadratic models using U.S. and Japanese LIBOR and swap rates and the exchange rate between the two economies. Estimation shows that independent currency factors are essential in releasing the tension between the currency movement and the term structure of interest rates. JEL Classification: G12, G13, E43 1.
F.: Interest rate caps smile too! But can the Libor market models capture it
 J. Financ., http://www.afajof.org/afa/forthcoming/2495.pdf
"... Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closedform formula for cap prices. We ..."
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Cited by 13 (2 self)
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Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closedform formula for cap prices. We show that although a threefactor stochastic volatility model can price atthemoney caps well, significant negative jumps in interest rates are needed to capture the smile. The volatility smile contains information that is not available using only atthemoney caps, and this information is important for understanding term structure models. THE EXTENSIVE LITERATURE ON MULTIFACTOR DYNAMIC term structure models (hereafter, DTSMs) of the last decade mainly focuses on explaining bond yields
Nonparametric Estimation of StatePrice Densities Implicit in Interest Rate Cap Prices
 Review of Financial Studies
, 2009
"... Based on a multivariate extension of the constrained locally polynomial estimator of AtSahalia and Duarte (2003), we provide nonparametric estimates of the probability densities of LIBOR rates under forward martingale measures and the stateprice densities (SPDs) implicit in interest rate cap price ..."
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Cited by 10 (1 self)
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Based on a multivariate extension of the constrained locally polynomial estimator of AtSahalia and Duarte (2003), we provide nonparametric estimates of the probability densities of LIBOR rates under forward martingale measures and the stateprice densities (SPDs) implicit in interest rate cap prices conditional on the slope and volatility factors of LIBOR rates. Both the forward densities and the SPDs depend signicantly on the volatility of LIBOR rates, and there is a signicant impact of mortgage prepayment activities on the forward densities. The SPDs exhibit a pronounced Ushape as a function of future LIBOR rates, suggesting that the state prices are high at both extremely low and high interest rates, which tend to be associated with periods of economic recessions and high in
ations, respectively. Our results provide nonparametric evidence of unspanned stochastic volatility and suggest that the unspanned factors could be partly driven by renancing activities in the mortgage markets. Overthecounter interest rate derivatives, such as caps and swaptions, are among the most widely traded interest rate derivatives in the world. According to the Bank for International Settlements, in recent years, the notional value of caps and swaptions exceeds $ 10 trillion, which is many times