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73
An Evaluation of MultiFactor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices
, 2001
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Correlation risk and the term structure of interest rates. Working paper
, 2008
"... We develop a structural model of the term structure of interest rates, in which state variables evolve as a matrixvalued process of stochastically correlated factors. This setting grants a new element of flexibility in the simultaneous modeling of stochastic volatilities and correlations of factors ..."
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Cited by 21 (2 self)
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We develop a structural model of the term structure of interest rates, in which state variables evolve as a matrixvalued process of stochastically correlated factors. This setting grants a new element of flexibility in the simultaneous modeling of stochastic volatilities and correlations of factors, and in the formulation of the market price of risk. We demonstrate that the model provides a unified answer to several empirical regularities of the yield curve such as the predictability of excess bond returns, the persistence of conditional volatilities and correlations of yields, and the humped term structure of forward rate volatilities. At the same time, it remains very parsimonious and analytically tractable with closedform solutions for zerocoupon bonds, and semi closedform solutions for the prices of interest rate derivatives.
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 21 (4 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.
Jump Starting GARCH: Pricing and Hedging Options with Jumps in Returns and Volatilities
, 2004
"... This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Limiting cases of our GARCH processes consist of models where both asset returns and local volatility follow jump diffusion processes with correlated jump si ..."
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Cited by 21 (0 self)
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This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Limiting cases of our GARCH processes consist of models where both asset returns and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of the GARCH models to their continuous time limits is extremely fast. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process. Since the state variables are fully determined by the path of prices, once the parameters have been estimated, option prices can readily be computed. We find that option prices, even 50 weeks after the parameters are estimated are fairly precise. In addition to pricing tests, we examine hedging effectiveness, and provide evidence that the hedges can be maintained very well over time.
OptionImplied Correlations and the Price of Correlation Risk, Working paper
, 2012
"... Motivated by extensive evidence that stockreturn correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing optionimplied correlations between stock returns (obtained by com ..."
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Cited by 18 (0 self)
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Motivated by extensive evidence that stockreturn correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing optionimplied correlations between stock returns (obtained by combining index option prices with prices of options on all index components) with realized correlations. Our parsimonious model shows that the substantial gap between average implied (38% for S&P500 and 44% for DJ30) and realized correlations (31% and 34%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that optionimplied correlations have remarkable predictive power for future stock market returns.
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 11 (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
On the information in the interest rate term structure and option pricesâ€™, Review of Derivatives Research
, 2004
"... Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an optionimplied interest rate covariance m ..."
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Cited by 7 (1 self)
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Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an optionimplied interest rate covariance matrix from cap and swaption prices, we use Libor market models and discretetenor string models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard lowfactor term structure models. The empirical analysis is based on weekly US data from 1995 to 1999. Our empirical results show that the option prices imply a covariance matrix of interest rates that is significantly different from the covariance matrix implied by realized interest rate changes. In particular, if one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.
Interest Rate Model Calibration Using Semidefinite Programming
, 2003
"... We show that, for the purpose of pricing Swaptions, the Swap rate and the corresponding Forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and an approximation formula is derived for such options. This ..."
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Cited by 6 (0 self)
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We show that, for the purpose of pricing Swaptions, the Swap rate and the corresponding Forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and an approximation formula is derived for such options. This formula is centered around a BlackScholes price with an appropriate volatility, plus a correction term that can be interpreted as the expected tracking error. The calibration problem can then be solved very efficiently using semidefinite programming.
RiskManagement Methods for the Libor Market Model Using Semidefinite Programming
, 2003
"... When interest rate dynamics are described by the Libor Market Model as in Brace, Gatarek & Musiela (1997), we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption's price, we ..."
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Cited by 6 (0 self)
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When interest rate dynamics are described by the Libor Market Model as in Brace, Gatarek & Musiela (1997), we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption's price, we show that the optimal dual variables describe a hedging portfolio in the sense of Avellaneda & Paras (1996). In the general case, the local sensitivity of the covariance matrix to all market movement scenarios can be directly computed from the optimal dual solution. We also show how semidefinite programming can be used to manage the Gamma exposure of a portfolio.