No-arbitrage Model Research Articles

On Pricing Credit Default Swaps with Observable Covariates

Observable covariates are useful for predicting default under the natural measure, but several findings question their value for explaining credit spreads under the pricing measure. We introduce a discrete time no-arbitrage model with observable covariates, which allows for a closed form solution for the value of credit default swaps (CDS). The default intensity is a quadratic function of the covariates, specified such that it is always positive. The model yields economically sensible results in terms of fit, economic impact of coefficients, and statistical significance. Macroeconomic and firm-specific information can explain most of the variation in CDS spreads over time and across firms, even with a parsimonious specification. These findings resolve the existing disconnect in the literature regarding the value of observable covariates for credit risk pricing and default prediction. Our results also suggest that although CDS spreads are highly auto-correlated, analyzing spread levels may be preferable to analyzing differences for daily CDS data.

Core and 'Crust': Consumer Prices and the Term Structure of Interest Rates

We propose a no-arbitrage model that jointly explains the dynamics of consumer prices as well as the nominal and real term structures of risk-free rates. In our framework, distinct core, food, and energy price series combine into a measure of total inflation to price nominal Treasuries. This approach captures different frequencies in inflation fluctuations: Shocks to core are more persistent and less volatile than shocks to food and, especially, energy (the 'crust'). We find that a common structure of latent factors determines and predicts the term structure of yields and inflation. The model outperforms popular benchmarks and is at par with the Survey of Professional Forecasters in forecasting inflation. Real rates implied by our model uncover the presence of a time-varying component in TIPS yields that we attribute to disruptions in the inflation-indexed bond market. Finally, we find a pronounced declining pattern in the inflation risk premium that illustrates the changing nature of inflation risk in nominal Treasuries.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2192271

Understanding the Real Rate Conundrum: An Application of No-Arbitrage Models to the UK Real Yield Curve*

During 2004 and 2005, long-horizon interest rates fell sharply in major international government bond markets (Greenspan's conundrum). This common fall mainly reflected lower long real rates. To investigate possible causes, the authors apply a no-arbitrage affine modeling framework to understanding the UK real term structure. The authors find that time-varying term premia are important in explaining movements in long real forward rates. And, although there is evidence that long-horizon expected short real rates declined over the conundrum period, the authors' results suggest that lower term premia played the dominant role. This could be consistent with the so-called search for yield and excess liquidity explanations for the conundrum. Copyright 2011, Oxford University Press.

A Global Model of International Yield Curves: No-Arbitrage Term Structure Approach

This paper extends a popular no-arbitrage affine term structure model to model jointly bond markets and exchange rates across the United Kingdom, United States and euro area. Using a monthly data set of forward rates from 1992, we first demonstrate that two global factors account for a significant proportion in the variation of bond yields across countries. We also show that, in order to explain country-specific movements in yield curves, local factors are required. Although we implement a very general factor structure, we find that our global factors are related to global inflation and global economic activity, while local factors are closely linked to monetary policy rates. In this respect our results are similar to previous work. But an important advantage of our joint international model is that we are able to decompose interest rates into risk-free rates and risk premia. Additionally, we are able to study the implications for exchange rates. We show that while differences in risk-free rates matter, to a large extent changes in the exchange rate are determined by time-varying exchange rate risk premia.

New Efficient Frontier: Can Structured Products Really Improve Risk-Return Profile

In this paper we investigate the contribution of structured bonds to the efficient frontier. We conduct our analysis by simulating the term structure according to a no-arbitrage multifactor model (G2 ) and comparing the performance of basic products (like zero-coupon bond, coupon bond and floating rate notes) with respect to more sophisticated products (like cms, collars, spread and volatility notes). In particular, our analysis considers different initial market environment like interest rate term structure shapes, as well as volatility and correlation in its changes and takes into account how the combined effect of risk-premium required by investors and fees that they have to pay can change the portfolio allocation respect to the one made only of basic securities. Our simulation results show that structured products can be an interesting investment only under particular scenarios. However, in general the return net of the fees in these securities is in average lower than the return in basic securities.

Monetary Policy Shifts and the Term Structure

We estimate the effect of shifts in monetary policy using the term structure of interest rates. In our no-arbitrage model, the short rate follows a version of the Taylor's (1993, “Discretion Versus Policy Rules in Practice”, Carnegie-Rochester Conference Series on Public Policy, 39, 195–214) rule where the coefficients on the output gap and inflation vary over time. The monetary policy loading on the output gap has averaged around 0·4 and has not changed very much over time. The overall response of the yield curve to output gap components is relatively small. In contrast, the inflation loading has changed substantially over the last 50 years and ranges from close to zero in 2003 to a high of 2·4 in 1983. Long-term bonds are sensitive to inflation policy shifts with increases in inflation loadings leading to higher short rates and widening yield spreads.

Inflation Risk Premia in the Term Structure of Interest Rates: Evidence from Euro Area Inflation Swaps

We estimate inflation risk premia in the Euro area using inflation swaps. By proposing a no-arbitrage model for econometric analysis, and estimating it using Markov Chain Monte Carlo, we find estimates of inflation risk premia, that on average show an upward sloping term structure, with 1 year risk premia of 13 bps and 10 year risk premia of 52 bps, however with fluctuation in risk premia over time. Our estimates suggest that surveys are important in identifying inflation expectations and thus inflation risk premia. We relate estimates of inflation risk premia to agents beliefs, and find that skews in short term inflation perceptions drive short term inflation risk premia, where beliefs on GDP growth drive longer term risk premia.

The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk

In light of the growing importance of the variable annuities market, in this paper we introduce a theoretical model for the pricing and valuation of guaranteed lifelong withdrawal benefit (GLWB) options embedded in variable annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy because if the account value becomes zero while the insured is still alive, he or she continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit. We offer a specific framework to value the GLWB option in a market-consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, which extend the Black-Scholes framework to insurance contracts, assuming the fund follows a geometric Brownian motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk-free rate, and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed, and numerical results are provided.

Mercados futuro e à vista de açúcar: uma análise empírica de eficiência versus arbitragem

Este trabalho testa a hipótese de eficiência relativa dos mercados futuro e à vista (spot) de açúcar, para dois horizontes de previsão, em contraposição à hipótese de arbitragem de commodities. Utiliza-se o modelo de não-arbitragem de Brenner e Kroner (1995) e aplica-se a metodologia de testes comparativos proposta por Kellard (2002), que usa a cointegração multivariada com restrição sobre o espaço de cointegração. A base de dados é formada a partir dos futuros do contrato número 11 negociado na Nybot (New York Board of Trade), dos preços no mercado à vista coletados pelo Cepea (Centro de Estudos Avançados em Economia Aplicada) e da taxa de juros doméstica, todas em bases diárias (mai/97 a dez/07). A correspondência da amostra é construída de acordo com os vencimentos dos contratos, considerando-se dois períodos de previsão: 28 e 56 dias. Em linhas gerais, as evidências empíricas encontradas suportam a adequação da metodologia de cointegração para análise de eficiência relativa nos mercados de açúcar, em contraposição à hipótese de arbitragem. Além disso, geram evidências fracas de ineficiência, resultados sujeitos à hipótese de estacionariedade do custo de carregamento, exceto pelo componente taxa de juros.

G10 Swap and Exchange Rates

This paper develops a simple no-arbitrage model of foreign exchange rates and interest rates that can easily be applied to an arbitrary number of foreign currencies. The model has the appealing feature that it reduces to a standard two or three factor model for pricing yields in each currency, yet it can still accommodate a small number of globally priced risk factors. We use the model to analyze the joint dynamics of exchange rates and the term structures of swap rates for the G10 currencies. Using both in- and out-of-sample measures of fit we conclude that there is one priced risk factor in G10 swap rates. We estimate the risk premium for exposure to this single factor and show that a U.S. fixed income investor can roughly double the Sharpe ratio of her portfolio if she is willing/able to invest in any yield in any G10 currency.

Long-Run Consumption Risk and the Real Yield Curve

This paper estimates a consumption-based, no-arbitrage model of the term structure of real interest rates. The model nests the standard long-run risk model which assumes constant market prices of risk. We find that the long-run consumption risk dominates the short-run and volatility risks and drives most of the movements of bond risk premiums. The risk premium for consumption volatility is negative, suggesting that long-term real bonds provide an effective hedge against the volatility risk in consumption growth. In contrast to the standard long-run risk model, however, we find strong evidence that the market price of long-run consumption risk is time-varying and that stochastic volatilities alone are not sufficient to account for the variations in bond risk premiums.

Monetary Policy Shifts and the Term Structure

We estimate the effect of shifts in monetary policy using the term structure of interest rates. In our no-arbitrage model, the short rate follows a version of the Taylor (1993) rule where the coefficients on inflation and output can vary over time. We find that monetary policy loadings on inflation, but not output, changed substantially over the last 50 years. Agents tend to assign a risk discount to monetary policy shifts and are willing to pay to be exposed to activist monetary policy. Over 1952-2006, if agents had assigned no value to active monetary policy, the slope of the yield curve would have been approximately 50 basis points higher, and up to twice as volatile, than what actually occurred in data.

Information in the Term Structure of Yield Curve Volatility

We decompose conditional volatilities of US Treasury yields into components due to short-rate expectations and term premia. To this end, we propose a novel no-arbitrage model which we estimate with extensive second-moment data. Short-rate expectations become more volatile than premia before recessions and during asset market distress. The correlation between shocks to premia and expectations is close to zero on average and varies with stance of monetary policy. While Treasuries are nearly unexposed to variance shocks, investors pay a large premium for hedging variance risk with derivatives. We illustrate the distinct dynamics of those yield volatility components during and after the financial crisis.

Risk Aversion, Intertemporal Substitution, and the Term Structure of Interest Rates

We build and estimate an equilibrium model of the term structure of interest rates based on a recursive utility specification. We contrast it with an arbitrage-free model, where prices of risk are estimated freely without preference constraints. In both models, nominal bond yields are affine functions of macroeconomic state variables. The equilibrium model accounts for the tent-shaped pattern and magnitude of coefficients from predictive regressions of excess bond returns on forward rates and the hump-shaped pattern in the term structure of volatilities, while the reduced-form no-arbitrage model does not account for these important features of the yield curve.

Nominal Interest Rates and the News

This paper provides new estimates of the impact of monetary policy actions and macroeconomic news on the term structure of nominal interest rates. The key novelty is to parsimoniously capture the impact of news on all interest rates using a simple no-arbitrage model. The different types of news are analyzed in a common framework by recognizing their heterogeneity, which allows for a systematic comparison of their effects. This approach leads to novel empirical findings: First, monetary policy causes a substantial amount of volatility in both short-term and long-term interest rates. Second, macroeconomic data surprises have small and mostly insignificant effects on the long end of the term structure. Third, the term-structure response to macroeconomic news is consistent with considerable interest-rate smoothing by the Federal Reserve. Fourth, monetary policy surprises are multidimensional while macroeconomic surprises are one-dimensional.

Currency Investing in Global Portfolios: Hedging or Speculative Benefits?

Currency risk hedging typically aims at minimizing portfolio volatility. We find that while hedging lowers the volatility of international equity and bond portfolios, it also lowers portfolio returns. Furthermore, Sharpe ratios often deteriorate, portfolio skewness worsens and its kurtosis increases. In a no-arbitrage model of interest rates and exchange rates with an equity component, currency expected returns are positively related to the covariance between currency and equity returns. Consequently, the hedge goes short in currencies with positive expected returns. The model also generates the observed negative effects of hedging on Sharpe ratios and skewness. In sum, currency hedging is no free lunch.

The Cross-Section and Time-Series of Stock and Bond Returns

We show that bond factors which predict future U.S. economic activity at business cycle horizons are priced in the cross-section of U.S. stock returns. High book-to-markets stocks have larger exposures to these bond factors than low book-to-market stocks, because their cash flows are more sensitive to the business cycle. Because of this new nexus between stock and bond markets, a parsimonious three-factor dynamic no-arbitrage model can be used to jointly price book-to-market-sorted portfolios of stocks and maturity-sorted bond portfolios, while reproducing the time-series variation in expected bond returns. The business cycle itself is a priced state variable in stock and bond markets.

Strong consistency of maximum likelihood estimators for a discrete-time random field HJM-type interest rate model

We consider a discrete time Heath–Jarrow–Morton-type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency of maximum likelihood estimators is proved for stable and unstable no-arbitrage models containing a simple stochastic discounting factor.

Affine General Equilibrium Models

No-arbitrage models are extremely flexible modelling tools but often lack economic motivation. This paper describes an equilibrium consumption-based CAPM framework based on Epstein-Zin preferences, which produces analytic pricing formulas for stocks and bonds under the assumption that macro growth rates follow affine processes. This allows the construction of equilibrium pricing formulas while maintaining the same flexibility of state dynamics as in no-arbitrage models. In demonstrating the approach, the paper presents a model that incorporates inflation such that asset prices are nominal. The model takes advantage of the possibility of non-Gaussian shocks and model macroeconomic uncertainty as a jump-diffusion process. This leads to endogenous stock market crashes as stock prices drop to reflect a higher expected rate of return in response to sudden increases in risk. The nominal yield curve in this model has a positive slope if expected inflation growth negatively impacts real growth. This model also produces asset prices that are consistent with observed data, including a substantial equity premium at moderate levels of risk aversion.

The Term Structure of Interest-Rate Futures Prices

We derive general properties of two-factor models of the term structure of interestrates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. In this model, the term structure shifts and tilts as the factor rates vary. The cross-sectional propertiesof the model derive from the solution of a two-dimensional, autoregressive process for the short-term rate, which exhibits both mean-reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatilities and the correlations ofthe futures rates of various maturities. These are shown to be related to the volatility of the short rate, the volatility of the second factor, the degree of mean-reversion and the persistence of the second factor shock. We also discuss the extension of our model to three or more factors. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate (LIBOR)] follows atwo-dimensional process. We calibrate the model using data from Eurocurrencyinterest rate futures contracts, using alternative optimization criteria. We then derive the term structures of volatilities and correlations implied by the model.