No-arbitrage Model Research Articles

Canonical Term-Structure Models with Observable Factors and the Dynamics of Bond Risk Premiums

We derive a canonical representation for the no-arbitrage discrete-time term structure models with both observable and unobservable state variables, popularized by Ang and Piazzesi (2003). We conduct a specification analysis based on this canonical representation and we analyze how alternative parametrizations affect estimated risk premia, impulse response functions and variance decompositions. We find a trade-off between the need to obtain parsimonious parametrizations and the ability of the models to match observed patterns of variation in risk premia. We also find that more richly parametrized models uncover a greater influence of macroeconomic fundamentals on the long-end of the yield curve.

Common Risk Factors in Currency Markets

We identify a ‘slope’ factor in exchange rates. High interest rate currencies load more on this slope factor than low interest rate currencies. This factor accounts for most of the cross-sectional variation in average excess returns between high and low interest rate currencies. A standard, no-arbitrage model of interest rates with two factors – a country-specific factor and a global factor – can replicate these findings, provided there is sufficient heterogeneity in exposure to global or common innovations. We show that our slope factor identifies these common shocks, and we provide empirical evidence that it is related to changes in global equity market volatility. By investing in high interest rate currencies and borrowing in low interest rate currencies, US investors load up on global risk.

A Macro‐Finance Model of the Term Structure, Monetary Policy and the Economy

This paper develops and estimates a macro-finance model that combines a canonical affine no-arbitrage finance specification of the term structure with standard macroeconomic aggregate relationships for output and inflation. From this new empirical formulation, we obtain several interesting results: (1) the latent term structure factors from finance no-arbitrage models appear to have important macroeconomic and monetary policy underpinnings, (2) there is no evidence of monetary policy inertia or a slow partial adjustment of the policy interest rate by the Federal Reserve, and (3) both forward-looking and backward-looking elements play important roles in macroeconomic dynamics.

Term Structure Forecasting: No-Arbitrage Restrictions versus Large Information Set

This paper addresses the issue of forecasting the term structure. We provide a unified state-space modelling framework that encompasses different existing discrete-time yield curve models. Within such framework we analyze the impact of two modelling choices, namely the imposition of no-arbitrage restrictions and the size of the information set used to extract factors, on the forecasting performance. Using US yield curve data, we find that both no-arbitrage and large info help in forecasting but no model uniformly dominates the other. No-arbitrage models are more useful at shorter horizon for shorter maturities. Large information sets are more useful at longer horizons and longer maturities. We also find evidence for a significant feedback from yield curve models to macroeconomic variables that could be exploited for macroeconomic forecasting.

A Black Swan in the Money Market

At the center of the financial market crisis of 2007-2008 was a highly unusual jump in spreads between the overnight inter-bank lending rate and term London inter-bank offer rates (Libor). Because many private loans are linked to Libor rates, the sharp increase in these spreads raised the cost of borrowing and interfered with monetary policy. The widening spreads became a major focus of the Federal Reserve, which took several actions--including the introduction of a new term auction facility (TAF)--to reduce them. This paper documents these developments and, using a no-arbitrage model of the term structure, tests various explanations, including increased risk and greater liquidity demands, while controlling for expectations of future interest rates. We show that increased counterparty risk between banks contributed to the rise in spreads and find no empirical evidence that the TAF has reduced spreads. The results have implications for monetary policy and financial economics.

The Risk-Neutral Hedging Strategy Based on Market-Index, Index-Futures and Index-Options - A Case Study

This paper reveals the frontier no-arbitrage hedge model based on market index, index futures and index options of stocks. Compared the risk-neutral density function estimated from the cross sections of market index and index futures to the risk-neutral density function inferred from the time series of index options market of stocks, use non-parametric method and hypothesis test, furthermore to capture the arbitrage opportunity and design the hedge strategies which are non-linear. Through the comparison between the high-degree moments of the above two density functions, it is noted that the hedging opportunity and the strategy for designing transaction, three moments Skewness transaction and four moments Kurtosis transaction can be applied. Through the simulation transaction analysis on the case in SP500, it is discovered that the Sharp ratios of these two transactions strategies are completely different from the strategy used to forecast the market trends through the index fund of invested market index.

Macro Variables Do Drive Exchange Rate Movements: Evidence from a No-Arbitrage Model

Expected exchange rate changes are determined by interest rate differentials across countries and risk premia, while unexpected changes are driven by innovations to macroeconomic variables, which are amplified by time-varying market prices of risk. In a model where short rates respond to the output gap and inflation in each country, I identify macro and monetary policy risk premia by specifying no-arbitrage dynamics of each country's term structure of interest rates and the exchange rate. Estimating the model with US/German data, I find that the correlation between the model-implied exchange rate changes and the data is over 60%. The model implies a countercyclical foreign exchange risk premium with macro risk premia playing an important role in matching the deviations from Uncovered Interest Rate Parity. I find that the output gap and inflation drive about 70% of the variance of forecasting the conditional mean of exchange rate changes.

The Dynamics of Risk Premiums in Nord Pool's Futures Market

The existence of premiums in futures prices has been the subject of much debate. This debate has centered around two views: the no-arbitrage model or theory of storage, and the equilibrium approach, sometimes called the theory of normal backwardation. The no-arbitrage approach equates the futures price to the spot price, storage cost and convenience yield. One can see immediately that it is difficult at best to apply this approach to electricity markets, where the underlying commodity is non-storable. Storage costs and convenience yield either become infinite or lose their meaning. It is of particular interest, then, to examine these prices from the equilibrium approach, which splits futures prices into an expected spot price component and a risk premium component. (Fama and French, 1987)

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 version of the Bansal & Yaron (2004) model which maintains a positive volatility process, as well as an example in which the volatility process is allowed to jump. The latter produces endogenous asset stock market crashes as stock prices drop to reflect a higher expected rate of return in response to increased risk. A third generalization is a model of nominal stock and bond prices. The nominal yield curve in this model has 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.

Empirically Confronting Stochastic Singularity: An Application to the Cox, Ingersoll, and Ross Model

We just-identify a no-arbitrage term structure model in estimation and then test it using both a classical orthogonality restriction test and a test of conditional predictive ability. We treat the error structure as unmodeled heterogeneity so that the model is estimated without errors, and the statistical question is whether using the model to characterize the dynamics and patterns in historical data is either useful or optimal as a forecasting tool. The data we use are from the transparent Greenspan regime at the Fed (1989-2005), and we also use a rolling estimation format so that regime shifts are not a likely cause of the model's performance. Substantively we find that the model is not a good forecasting device for short rates which in this period are strongly affected by changes in the target Fed Funds rate. For longer term rates, especially at longer forecast horizons where Fed policy has no effect, the model is more informative.

A No-Arbitrage Analysis of Economic Determinants of the Credit Spread Term Structure

This paper presents an internally consistent analysis of the economic determinants of the term structure of credit spreads across different credit rating classes and industry sectors. Our analysis proceeds in two steps. First, we extract three economic factors from 13 time series that capture three major dimensions of the economy: inflation pressure, real output growth, and financial market volatility. In the second step, we build a no-arbitrage model that links the dynamics and market prices of these fundamental sources of economic risks to the term structure of Treasury yields and corporate bond credit spreads. Via model estimation, we infer the market pricing of these economic factors and their impacts on the whole term structure of Treasury yields and credit spreads. Estimation shows that positive inflation shocks increase both Treasury yields and credit spreads across all maturities and credit rating classes. Positive shocks on the real output growth also increase the Treasury yields, more so at short maturities than at long maturities. The impacts on the credit spreads are positive for high credit rating classes, but become negative and increasingly so at lower credit rating classes. The financial market volatility factor has small positive impacts on the Treasury yield curve, but the impacts are strongly positive on the credit spreads, and increasingly so at longer maturities and lower credit rating classes. Finally, when we divide each rating class into two industry sectors: financial and corporate, we find that with in each rating class, the credit spreads in the financial sector are on average wider and more volatile than the spreads in the corporate sector. Estimation further shows that the term structure of credit spreads in the financial sector is more responsive to shocks in the economic factors.

Volatility transmission between stock and bond markets

A two-factor no-arbitrage model is used to provide a theoretical link between stock and bond market volatility. While this model suggests that short-term interest rate volatility may, at least in part, drive both stock and bond market volatility, the empirical evidence suggests that past bond market volatility affects both markets and feeds back into short-term yield volatility. The empirical modelling goes on to examine the (time-varying) correlation structure between volatility in the stock and bond markets and finds that the sign of this correlation has reversed over the last 20 years. This has important implications far portfolio selection in financial markets.

An affine three-factor model of the German term structure of interest rates with macroeconomic content

This paper extends the empirical no-arbitrage Gaussian affine term structure model of Cassola and Luis (2003) in a way that leads to a Taylor rule expression for the short rate dynamics. The empirical results indicate that the dynamics of the German term structure of interest rates can be sufficiently explained by expected variations in inflation and output plus an additional unobservable factor. The novelty is that we are able to extract a monetary policy reaction function within this no-arbitrage model that closely resembles empirical reaction functions based on the dynamics of the short rate only.

Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models

A widespread approach in the implementation of asset pricing models is based on the periodic recalibration of its parameters and initial conditions to eliminate any conflict between model-implied and market prices. Modern no-arbitrage market models facilitate this procedure since their solution can usually be written in terms of the entire initial yield curve. As a result, the model fits (by construction) the interest rate term structure. This procedure is, however, generally time inconsistent since the model at time t = 0 completely specifies the set of possible term structures for any t > 0. In this paper, we analyze the pros and cons of this widespread approach in pricing and hedging, both theoretically and empirically. The theoretical section of the paper shows (a) under which conditions recalibration improves the hedging errors by limiting the propagation of an initial error, (b) that recalibration introduces time-inconsistent errors that violate the self-financing argument of the standard replication strategy. The empirical section of the paper quantifies the trade-off between (a) and (b) under several scenarios. First, we compare this trade-off for two economies with and without model specification error. Then, we discuss the trade-off when the underlying economy is not Markovian.

A No-Arbitrage Analysis of Macroeconomic Determinants of the Credit Spread Term Structure

From a large array of economic and financial data series, this paper identifies three fundamental risk dimensions underlying an economy: inflation, real output growth, and financial market volatility. Furthermore, through a no-arbitrage model, the paper links the dynamics and market pricing of the three risk dimensions to the term structure of U.S. Treasury yields and corporate bond credit spreads. Model estimation shows that positive inflation shocks increase Treasury yields and widen credit spreads on corporate bonds across all maturities and credit-rating classes. Positive real output growth shocks also increase Treasury yields, but they suppress the credit spreads at low credit-rating classes, thus generating negative correlations between interest rates and credit spreads. The financial market volatility factor has a small and transient effect on the Treasury yield curve, but it exerts a strongly positive and persistent effect on the credit spread term structure. The paper provides a robust and internally consistent method for extracting systematic economic information from a large array of noisy observations and establishing how different risk dimensions of the fundamental economy interact with interest rate and credit risk.

The Recent Shift in Term Structure Behavior from a No-arbitrage Macro-finance Perspective

This paper examines a recent shift in the dynamics of the term structure and interest rate risk. We first use standard yield-spread regressions to document such a shift in the U.S. in the mid-1980s. Over the pre- and post-shift subsamples, we then estimate dynamic, affine, no-arbitrage models, which exhibit a significant difference in behavior that can be largely attributed to changes over time in the pricing of risk associated with a level factor. Finally, we suggest a link between the shift in term structure behavior and changes in the risk and dynamics of the inflation target as perceived by investors.

A Macro-Finance Model of the Term Structure, Monetary Policy, and the Economy

This paper develops and estimates a macro-finance model that combines a canonical affine no-arbitrage finance specification of the term structure with standard macroeconomic aggregate relationships for output and inflation. From this new empirical formulation, we obtain several important results: (1) the latent term structure factors from finance no-arbitrage models appear to have important macroeconomic and monetary policy underpinnings, (2) there is no evidence of monetary policy inertia or a slow partial adjustment of the policy interest rate by the Federal Reserve, and (3) both forward-looking and backward-looking elements play important roles in macroeconomic dynamics.

Towards a Joint Characterization of Monetary Policy and the Dynamics of the Term Structure of Interest Rates

The paper develops an empirical no-arbitrage Gaussian affine term structure model to explain the dynamics of the German term structure of interest rates from 1979 through 1998. In contrast to most affine term structure models two risk factors that drive the dynamics are linked to observable macroeconomics factors: output and inflation. The results obtained by a Kalman-filter-based maximum likelihood procedure indicate that the dynamics of the German term structure of interest rates can be sufficiently explained by expected variations in those macroeconomic factors plus an additional unobservable factor. Furthermore, we are able to extract a monetary policy reaction function within this no-arbitrage model of the term structure that closely resembles the empirical reaction functions that are based on the dynamics of the short rate only.

Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment

The success over the years in reducing inflation and, consequently, the average level of nominal interest rates has increased the likelihood that the nominal policy interest rate may become constrained by the zero lower bound. When that happens, a central bank can no longer stimulate aggregate demand by further interest-rate reductions and must rely on \non-standard policy alternatives. To assess the potential effectiveness of such policies, we analyze the behavior of selected asset prices over short periods surrounding central bank statements or other types of financial or economic news and estimate \no-arbitrage models of the term structure for the United States and Japan. There is some evidence that central bank communications can help to shape public expectations of future policy actions and that asset purchases in large volume by a central bank would be able to affect the price or yield of the targeted asset.

Analytical implementation of the Ho and Lee model for the short interest rate

Ho and Lee introduced the first no-arbitrage model of the evolution of the short interest rate. When expositing the Ho and Lee model, other authors used the method of numerical solutions and forward induction, an approach pioneered by Black, Derman, and Toy for their own model much later. This standard method of implementation is relatively complex and time consuming when applied to scenarios that enable the use of an interest-rate lattice. Under many assumptions, however, the Ho and Lee model will generate an interest-rate tree. Under these circumstances, implementation via numerical methods and forward induction appears to be impractical, if not impossible. In this paper, we show how to implement the model analytically. We demonstrate that it is relatively straightforward to identify at the initial date analytical expressions for all interest rates at all dates. Once these expressions are evaluated, the calculations to obtain interest rates are arithmetic operations. Our recommended method of implementation applies equally effortlessly to interest-rate trees and Monte Carlo simulation.