Essays on term structure and monetary policy

Abstract: This dissertation treats two different themes. The first, addressed in Chapter 1, regards the pricing of interest rate swaps. The second, studied in the remaining two chapters, regards the implications of monetary policy for the term structure of interest rates.The pricing of interest rate swaps An interest rate swap is an agreement between two parties to exchange fix for floating interest rate payments for a certain period of time. Floating rate payments are made at a floating-rate index, e.g. the three-month interbank rate, while the fixed rate payment, the swap rate, is determined on the market. The swap rate may include a compensation for credit risk depending on the counterparty's credit quality, but in the standard agreement there is no exchange of principal, only interest is transacted, and this effectively reduces concerns about credit risk. The swap spread for a given maturity is the difference between the swap rate and the risk-free rate, measured as the yield on a government bond with similar cash flows. If the standard swap agreement entails negligible credit risk one might expect swap spreads to be low and stable, but market swap spreads vary over time. There are periods when swap spreads are low in accordance with the general theory, but there are also periods when swap spreads reach levels that seem high.The first chapter of this dissertation examines a setting where a positive swap spread arises as part of an equilibrium in a perfectly competitive capital market. The model is one of insurance under adverse selection. A firm that seeks debt financing can insure itself against interest rate risk either by borrowing long-term or by borrowing short-term and entering a pay fix - receive float interest rate swap. The latter alternative allows for a partial hedge as the firm can choose to swap only a fraction of the nominal amount. In this setting, if firms' credit quality and interest rate risk tolerance are correlated creditors can use the pricing of interest rate swaps as a screening device. A low-risk firm, being a firm with favorable private information, selects short-term borrowing and partial insurance. A high-risk firm, being a firm with less favorable prospects, is by assumption also less risk tolerant. It therefore has a higher demand for insurance and the equilibrium swap spread is set such that the high-risk firm finds it more beneficial to borrow long-term at a cost that exceeds the expected cost from short-term financing, but that provides a full insurance to interest rate risk. Monetary policy and the term structure of interest rates Taken separately monetary policy and term structure modeling are two well-established research areas each comprising a substantial amount of research. But relatively few attempts have been made to integrate the two. The last two chapters of this dissertation take the view that the conduct of monetary policy is an essential element in the determination of the term structure of interest rates, and that explicitly considering the role of amonetary authority in the analysis has a potential of enhancing our understanding of term structure dynamics, and its relation to macro-economic fundamentals in particular. This approach to the term structure is supported by the fact that the analytical framework developed in the literature on optimal monetary policy translates conveniently into a setting well suited for term structure analysis. Chapter 2 makes the point in the simplest setting. A standard model of optimal monetary policy is reformulated in continuous time. Combined with a parameterized form for the market price of risk this produces a standard term structure model with well-known characteristics. This model is estimated on US data for the period 1987 - 2002, treating state variables as latent factors of the term structure. The parameters that are estimated comprise parameters describing the monetary transmission mechanism, parameters describing the monetary authority's preferences and parameters describing the market price of risk. Our estimation technique differs from comparable estimations in the monetary policy literature as these typically take state variables to be directly observable measures of macro-economic aggregates. The results using term structure data are both similar and different to previous findings. The main difference when using term structure data is that the central bank's estimated policy is more aggressive, i.e. more responsive to changes in the underlying state variables.Chapter 3 is devoted to the zero bound on nominal interest rates. While the zero bound is well recognized in the literature on term structure modeling, not much has been said about term structure dynamics under the special circumstance that the short rate is close to zero. I find the optimal monetary policy approach to be particularly well suited for this analysis. The chapter studies a continuous time reduced form version of the monetary transmission mechanism. The monetary authority's optimization problem is formed according to two specifications, interest rate stabilization and interest rate smoothing. For the former the optimization problem is solved analytically, while numerical procedures are adopted forthe latter. The chapter then turns to study implications for the term structure under risk-neutrality. Term structure equations are solved numerically and implications for the term structure are discussed. Data for a low-interest rate country like Japan for 1996 - 2003 exhibits s-shaped yield curves and yield volatility curves. This shape is found to be consistent with a smoothing objective for the short rate.