Narrow Results

This paper aims to establish a set of necessary and sufficient conditions that the expression of a default free bond must verify in a situation in which spot rates of interest increase. In this case, if the agent divides the period of his investment, that is, if he disinvests and, immediately, re-invests his capital in different issues of bonds, can obtain an advantage in the final amount. In order to do this, necessary conditions include an approximation of the forward interest rate, that is to say the logarithmic density, its limits to +∞ and -∞ and the second generalized derivative of the bond price. Sufficient conditions involve an auxiliary function using these limits and, finally, necessary and sufficient conditions are related with the logarithm of the bond price.

This paper uses a new restriction imposed by the no-arbitrage condition on interest rate processes to estimate the parameters of the short-term rates for US, France, UK and Germany. A general process that nests almost all previous one-factor models is estimated. The results show that the volatility structure of US short-term rate is similar to the processes suggested by Duffie and Kahn [9] or Chan et al. [4] depending on the proxy used for the short-term rate and the time period covered by the study. The volatility structures of the short-term rates in France and Germany do not have constant elasticity with respect to the short-term rate, while the elasticity of UK's short-term rate is constant and equal to 1.5.

We will develop an efficient method for estimating a smooth nonnegative forward rate sequence using the market price of riskless bonds. This method is an improvement of the classical Carleton–Cooper's method based on standard least square method, which often generates a non-smooth forward rate sequence and hence is not used in practice. The method to be proposed in this paper is intended to resolve this difficulty. We will impose a smoothness condition while maintaining the fitting error within an acceptable level. The resulting optimization problem is shown to be convex in the region of interest. Therefore, we can calculate a globally optimal solution very fast by standard nonlinear programming algorithms. We will demonstrate that this method generates a smooth forward rate sequence at the expense of a very small increase of fitting error.

The paper focuses on the market equilibrium conditions in forward exchange quotes. By careful analysis of the market arbitrage conditions, market supply and demand, we construct the equilibrium ranges for bid and ask forward quotes separately. We present our analysis in a bid-ask cost structure setting, and directly tie the equilibrium and arbitrage conditions to specific trading strategies. We conclude that in equilibrium there will be no chance for one-way-arbitrage in foreign exchange and securities markets, provided that non-reversed traders are active and set the arbitrage boundaries. The framework we develop in the paper is convenient for academic study and practical use in currency and security markets.

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

In this paper, we consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general semimartingale. Second, the Heath–Jarrow–Morton (HJM) approach is extended with an additional component capturing those future jumps in the term structure which are visible from the current time. Third, the associated recovery scheme is as general as possible, it is only assumed to be nonincreasing. In this general setting, we derive generalized drift conditions which characterize when a given measure is a local martingale measure, thus yielding no asymptotic free lunch with vanishing risk (NAFLVR), the right notion for this large financial market to be free of arbitrage.