Exchange rate dynamics under alternative optimal interest rate rules

We explore the role of interest rate policy in the exchange rate determination process. Specifically, we derive exchange rate equations from interest rate rules that are theoretically optimal under a few alternative settings. The exchange rate equation depends on its underlying interest rule and its performance could vary across evaluation criteria and sample periods. The exchange rate equation implied by the interest rate rule that allows for interest rate and inflation inertia under commitment offers some encouraging results — exchange rate changes “calibrated” from the equation have a positive and significant correlation with actual data, and offer good direction of change prediction. Our exercise also demonstrates the role of the foreign exchange risk premium in determining exchange rates and the difficulty of explaining exchange rate variability using only policy based fundamentals.     

The term structure of policy rules

A formula is derived that links the coefficients of the monetary policy rule for the short-term interest rate to the coefficients of the implied affine equations for long-term interest rates. The formula predicts that an increase in the coefficients in the monetary policy rule will lead to an increase in the coefficients in the affine equations. Empirical evidence for such a prediction is provided. The curve of the response coefficients by maturity is also predicted by the formula. The formula's predictive accuracy and its closed form make it a useful tool for studying the policy implications of embedding no-arbitrage affine theories into macro models.     

Regulation and the Neo-Wicksellian Approach to Monetary Policy

Laubach and Williams (2003) employ a Kalman filter approach to jointly estimate the neutral real federal funds rate and trend output growth using an IS relationship and an output-gap-based inflation equation. They find a positive link between these two variables, but also much error surrounding neutral real rate estimates. We modify their approach by including variables for regulations on deposit interest rates and on wages and prices. These variables are statistically significant and notably affect estimates of two policy-relevant coefficients: the sensitivity of output to the real interest rate and that of inflation to the output gap.     

Exchange rate dynamics under alternative optimal interest rate rules

We explore the role of interest rate policy in the exchange rate determination process. Specifically, we derive exchange rate equations from interest rate rules that are theoretically optimal under a few alternative settings. The exchange rate equation depends on its underlying interest rule and its performance could vary across evaluation criteria and sample periods. The exchange rate equation implied by the interest rate rule that allows for interest rate and inflation inertia under commitment offers some encouraging results — exchange rate changes “calibrated” from the equation have a positive and significant correlation with actual data, and offer good direction of change prediction. Our exercise also demonstrates the role of the foreign exchange risk premium in determining exchange rates and the difficulty of explaining exchange rate variability using only policy based fundamentals.     

Continuous-time term structure models: Forward measure approach

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and spot probability measures are introduced in this general set-up. Two conditions of no-arbitrage between bonds and cash are examined. A process of savings account implied by an arbitrage-free family of bond prices is identified by means of a multiplicative decomposition of semimartingales. The uniqueness of an implied savings account is established under fairly general conditions. The notion of a family of forward processes is introduced, and the existence of an associated arbitrage-free family of bond prices is examined. A straightforward construction of a lognormal model of forward LIBOR rates, based on the backward induction, is presented.     

A production-based model for the term structure

This paper considers the term structure of interest rates implied by a production-based asset pricing model in which the fundamental drivers are investment in equipment and structures as well as inflation. The model matches the average yield curve up to five-year maturity almost perfectly. Longer term yields are roughly as volatile as in the data. The model also generates time-varying bond risk premiums. In particular, when running Fama-Bliss regressions of excess returns on forward premiums, the model produces slope coefficients of roughly half the size of the empirical counterparts. Closed-form expressions highlight the importance of the capital depreciation rates for interest rate dynamics.     

Properties of foreign exchange risk premiums

We study the properties of foreign exchange risk premiums that can explain the forward bias puzzle, defined as the tendency of high-interest rate currencies to appreciate rather than depreciate. These risk premiums arise endogenously from the no-arbitrage condition relating the term structure of interest rates and exchange rates. Estimating affine (multi-currency) term structure models reveals a noticeable tradeoff between matching depreciation rates and accuracy in pricing bonds. Risk premiums implied by our global affine model generate unbiased predictions for currency excess returns and are closely related to global risk aversion, the business cycle, and traditional exchange rate fundamentals.     

The Banking View of Bond Risk Premia

Banks' balance sheet exposure to fluctuations in interest rates strongly forecasts excess Treasury bond returns. This result is consistent with optimal risk management, a banking counterpart to the household Euler equation. In equilibrium, the bond risk premium compensates banks for bearing fluctuations in interest rates. When banks' exposure to interest rate risk increases, the price of this risk simultaneously rises. We present a collection of empirical observations that support this view, but also discuss several challenges to this interpretation.     

Econometric models of the Eleventh District Cost of Funds Index

The Eleventh District Cost of Funds Index (COFI) is a popular index for pricing adjustable-rate mortgages. COFI is calculated from the interest expenses incurred by thrifts when raising funds. It is a mixture of current and past interest rates on many different financial instruments. COFI can be modelled well with simple econometric models. Commonly used, simple COFI models are compared using a method developed by Hendry (1989). Some of these models, which appear to fit the data well, have nonrobust parameters, significant serial correlation, and heteroscedastic errors. These poorly specified models may lead to systematic mispricing of COFI mortgages. Once a robust econometric model is chose, the lagged adjustment of COFI to movements in interest rates can be incorporated into mortgage pricing models.     

Interest Rate Risk and the Forward Premium Anomaly in Foreign Exchange Markets

This paper shows that even adjusted for the time-varying risk premiums implied by the yield curves across countries, uncovered interest parity is still strongly rejected by the data. Moreover, factors that predict the excess bond returns are found not significant at all in predicting the foreign exchange returns. These results reject the joint restrictions on the exchange rate and interest rates imposed by dynamic term-structure models, suggesting that foreign exchange markets and bond markets may not be fully integrated and we have to look beyond interest rate risk in order to understand the exchange rate anomaly.     

A generalized volatility bound for dynamic economies

We develop a generalization of the Hansen-Jagannathan (1991) volatility bound that (i) incorporates the serial correlation properties of return data and (ii) allows us to calculate a spectral version of the bound. This generalization enables us to judge whether models match important aspects of the data in the long run, at business cycle frequencies, seasonal frequencies, etc. Our bound permits evaluation of models without requiring their explicit solution in a way that respects the dynamic implications of the fundamental component of the models, namely, the Euler equation that links asset returns to the intertemporal marginal rate of substitution.     

The Central Banker as a Risk Manager: Estimating the Federal Reserve's Preferences under Greenspan

We derive a natural generalization of the Taylor rule that links changes in the interest rate to the balance of the risks implied by the dual objective of sustainable economic growth and price stability. This monetary policy rule reconciles economic models of expected utility maximization with the risk management approach to central banking. Within this framework, we formally test and reject the standard assumption of quadratic and symmetric preferences in inflation and output that underlies the derivation of the Taylor rule. Our results suggest that Fed policy decisions under Greenspan were better described in terms of the Fed weighing upside and downside risks to their objectives rather than simply responding to the conditional mean of inflation and of the output gap.     

Interest rate deregulation: Monetary policy efficacy and rate rigidity

This paper examines the effects of interest rate regulation, and subsequent deregulation, on the efficacy of monetary policy and rigidity of retail bank deposit rates in Hong Kong. Using an error-correction model, we find that interest rate deregulation increases the efficacy of monetary policy by improving the correlation between retail bank deposit rates and market interest rates and increasing the degree of long-term pass-through for retail bank deposit rates. Our study also shows that the adjustments in retail bank deposit rates are asymmetric and rigid upwards during the regulated period, but tend to be rigid downwards during the deregulated period. The spreads between retail bank deposit rates and market rates have also tightened sharply after the removal of interest rate controls.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.     

Inferring future volatility from the information in implied volatility in Eurodollar options: a new approach

We study the information content of implied volatility fromseveral volatility specifications of the Heath-Jarrow-Morton(1992) (HJM) models relative to popular historical volatilitymodels in the Eurodollar options market. The implied volatilityfrom the HJM models explains much of the variation of realizedinterest rate volatility over both daily and monthly horizons.The implied volatility dominates the GARCH terms, the Glostenet al. (1993) type asymmetric volatility terms, and the interestrate level. However, it cannot explain that the impact of interestrate shocks on the volatility is lower when interest rates arelow than when they are high.     

Monetary Policy and the Natural Rate of Interest

It is most important for monetary policy to track the natural rate of interest when interest rates take large and sustained swings away from their long‐run equilibrium values. Here, we study two models: a standard New Keynesian model and one in which government bonds provide liquidity. Policy rules that cannot track the natural rate perform poorly in both models, but are especially bad in the second because of sustained movements in the natural rate induced by fiscal shocks. First difference rules, on the other hand, do surprisingly well. When model uncertainty is taken into account, the dominance of the first difference rule is even more pronounced.     

Taylor rules, McCallum rules and the term structure of interest rates

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi [2002. The Fed and interest rates—a high-frequency identification. American Economic Review 92, 90-95.]. The result echoes the policy rule used by McCallum [1994a. Monetary policy and the term structure of interest rates. NBER Working Paper No. 4938.] to rationalize the empirical failure of the ‘expectations hypothesis’ applied to the term structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. McCallum showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. “yield-curve smoothing”), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss [1987. The information in long-maturity forward rates. The American Economic Review 77, 680-392.]. McCallum also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor [1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195-214.] Rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term-structure models studied in Duffie and Kan [1996. A yield-factor model of interest rates. Mathematical Finance 57, 405-443.]: a stochastic volatility model and a stochastic price-of-risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by McCallum (i.e., the “McCallum Rule”). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzessi [2003. A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics 50, 745-787.]). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and McCallum Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.     

The Liquidity Effect in the Federal Funds Market: Evidence at the Monthly Frequency

In this paper, we argue that much of the research into the link between money and interest rates suffers from misspecification. The measure of money and the measure of interest rates are not always well matched. In examining the transmission of monetary policy, we show that using an appropriate measure of money, Federal Reserve balances, and the appropriate interest rate, the federal funds rate, a clear liquidity effect exists. Furthermore, we explain how a lack of a clear institutional understanding may have contributed to the finding of a "liquidity puzzle" in the past.     

Quantifying the uncertainty about the fit of a new Keynesian pricing model

Recent studies by Gali and Gertler [1999. Inflation dynamics: a structural econometric analysis, Journal of Monetary Economics 44, 195-222] and Sbordone [2002. Prices and unit labor costs: testing models of pricing, Journal of Monetary Economics 49, 265-292] conclude that a theoretical inflation series implied by a forward-looking New Keynesian pricing equation fits post-1960 U.S. inflation closely. Their theoretical inflation series is conditional on (i) a reduced-form forecasting process for real marginal cost; and (ii) the calibration of the pricing equation. The present paper shows that both of these determinants are surrounded by considerable uncertainty. When quantifying the impact of this uncertainty on theoretical inflation, we can no longer say whether the forward-looking pricing equation explains observed inflation dynamics very well or very poorly.     

The impact of central bank digital currency variation on firm's implied volatility

The paper investigates whether a firm's implied volatility is affected by the volatility of central bank digital currencies. Our sample covers 2853 listed companies in the United States from 2014 to 2018. First, we find the variation of central bank digital currency has a positive impact on a firm’s implied volatility. Second, the healthier firms’ conditions can reduce the relationship between central bank digital currency variation and a firm’s implied volatility. Third, the positive relation between central bank digital currency and firm’s implied volatility still exists in investment-grade, speculative-grade, and unrated firms. Finally, to eliminate the endogeneity problem, we adopt simultaneous equation models (SEM) and find our results are still robust after excluding endogenous concerns. Our research provides a reminder for corporate managers and new implications for policymakers.