Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.     

Production and the Real Rate of Interest: A Sample Path Equilibrium

This paper examines a multiperiod production economy where investors do not observe the realizations of productivity factors or security expected returns. Unlike previous work, which expresses the equilibrium conditions as functions of unobservable (to both real-world investors and empiricists) moments of the distributions of returns, we express the equilibrium real rate as a function of the observable sample paths of realizations of returns. We provide a framework for empirically testing this and other asset pricing models without outside-the-model econometric assumptions needed for producing the unobservable moments of returns. We construct versions of the restrictions for any time interval between observations.     

On the determination of real interest rates in Europe

In this paper a loanable funds model is estimated over the period 1959–1990 for the determination of after-tax expected real interest rates using aggregated data for four European countries under the assumption that high capital mobility in Europe implies a common capital market. It is concluded that real interest rates in the European Community were mainly driven by movements in temporary income, expected inflation, lagged investment, money growth, and the oil price. Moreover, our aggregate, model appears to be reasonably stable. Finally, individual country rates are shown to depend on the European rate as well as some country-specific variables, suggesting a limited degree of isolation from international financial markets for the countries concerned.At the time of writing the author was still affiliated with the Department of Economics at the University of Groningen. Hence, any views expressed here are those of the author and do not necessarily represent those of De Nederlandsche Bank. This paper benefitted very much from stimulating comments made by Willem Buiter, Kanhaya Gupta, Jakob de Haan, Flip de Kam, Kees Koedijk, and an anonymous referee. The author would like to thank Jan-Egbert Sturm for technical assistence. Of course, the usual disclaimer applies.     

A Model of the Convenience Yields in On-the-Run Treasuries

The convenience yield differential between on- and off-the-run Treasury securities with identical maturities has two components. A non-cyclical component may arise due to the higher illiquidity of off-the-run bonds. Also, trading in the market for the next issue often causes cyclical shortages of the on-the-runs. When this occurs, owners of the on-the-run bond can earn riskless profits by borrowing at a special repo rate while lending at the prevailing risk free market rate. This second component of the convenience yield, induced by the auction, is cyclical. We first show that special repo rates and the convenience yield are jointly cyclical over the auction cycle. The patterns are statistically significant and pervasive. Repo specials are highest around the announcement day and disappear by the issue day. The off- minus on-the-run yield spread is highest at the beginning of the cycle and collapses near its end, consistent with a decreasing present value of profits over a decreasing horizon. Second, we develop a first no-arbitrage continuous-time model, with both interest and special repo rates stochastic, that prices the on-the-run bonds that command this convenience yield. A simple implementation of the model can generate yields consistent with the evidence.     

A New Approach to Markov-Switching GARCH Models

The use of Markov-switching models to capture the volatilitydynamics of financial time series has grown considerably duringpast years, in part because they give rise to a plausible interpretationof nonlinearities. Nevertheless, GARCH-type models remain ubiquitousin order to allow for nonlinearities associated with time-varyingvolatility. Existing methods of combining the two approachesare unsatisfactory, as they either suffer from severe estimationdifficulties or else their dynamic properties are not well understood.In this article we present a new Markov-switching GARCH modelthat overcomes both of these problems. Dynamic properties arederived and their implications for the volatility process discussed.We argue that the disaggregation of the variance process offeredby the new model is more plausible than in the existing variants.The approach is illustrated with several exchange rate returnseries. The results suggest that a promising volatility modelis an independent switching GARCH process with a possibly skewedconditional mixture density.     

European foreign exchange market efficiency: Evidence based on crisis and noncrisis periods

This study investigates the impact on foreign exchange market efficiency of the 1992 European financial market crisis by studying precrisis, crisis, and postcrisis periods. Long-term relationships among European currency values are identified during the three periods, although the relationships are not stable during the precrisis and the postcrisis periods. These results may be due to one or more of the following: (1) market inefficiency, (2) a risk premium, or (3) common policy guidelines for European monetary system (EMS) members. Evidence of market inefficiency is strong. Forecasting results demonstrate better performance by an error correction model (ECM) than by a random walk model (RWM) for the British pound and German mark, while results for the French franc and Italian lira are mixed. Dominance tests using Granger causality indicate only weak German mark dominance both in the short and long run.     

On the determinants of “small” and “large” foreign exchange market interventions: The case of the Japanese interventions in the 1990s

During the past 30 years, central banks have often intervened in foreign exchange markets, and the magnitude of their foreign exchange market interventions has varied widely. We develop a quantitative reaction function model that renders it possible to examine the determinants of “small” and “large” interventions. We apply the model to analyzing the intervention policy of the Japanese monetary authorities (JMA) in the yen/U.S. dollar market during the period from 1991 through 2001. To this end, we use recently released official data on the foreign exchange market interventions of the JMA. We find that the JMA tended to conduct large interventions when the yen/U.S. dollar exchange rate drifted away from an “implicit target exchange rate.”     

A Note on Forward Price and Forward Measure

The forward measure is convenient in calculating various contingent claim prices under stochastic interest rates. We demonstrate that caution needs to be drawn when the forward measure is used to price contingent claims that involve multiple cash flows. We also derive partial different equations for the forward price to demonstrate how forward contracts can be used for dynamic hedging and how hedges can be conducted if the payoff of a contingent claim depends on the forward price.     

An Assessment of Empirical Model Performance When Financial Market Transactions are Observed at Different Data Frequencies: An Application to East Asian Exchange Rates

This paper compares the performance of alternative models of east Asian exchange rates at different data frequencies. Selected models employ different specifications of the conditional variance and the conditional error distribution. Conditional variance specifications include: homoscedasticity, GARCH, LGARCH, and EGARCH. Conditional error distribution specifications include normal and Student t. The best exchange rate model specification is clearly conditional on data frequency. Higher frequency (daily, weekly) data commonly exhibit characteristics that demand more sophisticated estimation methods than analysts commonly employ. These characteristics generally vanish at lower (monthly, quarterly) frequencies. Overall we find significant benefit from accommodating heteroscedasticity and leptokurtic properties of the conditional distribution as data frequency increases. Using a likelihood ratio test we compare the relative gain from addressing heteroscedasticity (through use of GARCH models) versus accommodation of leptokurtosis. This comparison suggests that the gains from correct specification of the conditional distribution dominate those obtained from addressing problems of heteroscedasticity.     

The Relationships Between Mortgage Rates and Capital-Market Rates Under Alternative Market Conditions

Mortgage interest rates have become more integrated with other capital-market interest rates over recent decades, apparently as a result of the deregulation of financial markets. The link is both imperfect and time-varying. Mortgage rates during some time periods appear to be sticky with respect to their adjustment to changes in capital-market rates. We examine the relationship between weekly conventional mortgage rates and the interest rates on treasury and corporate securities under differing market conditions. We draw three conclusions based on the analysis. First, deregulation changed the link between mortgage rates and riskless interest rates, which confirms the findings of Goebel and Ma (1993). Second, mortgage rates were cointegrated with risky interest rates even before deregulation. Third, the link between mortgage rates and the risky bond rate can be associated with the behavior of the risk premium in the bond rate. The observed relationship is consistent with the stickiness observed by Haney (1988) and causes a more pronounced stickiness when rates are falling than when they are rising.