Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

Abstract

In this paper we study the convergence model of interest rates by Corzo and Schwartz. It models the situation when a country is going to enter a monetary union, for example the eurozone. We are interested in estimating the underlying short rate, which is a theoretical variable, not observed on the market. We use the procedure already employed for the Vasicek model to the eurozone data and for the case of a zero correlation we show that a similar procedure can be used also for the estimation of the domestic parameters and the short rate values. The assumption of the zero correlation allows us to simplify the optimization problem, but using simulations we show that our algorithm is robust to the specification of the correlation. It estimates the short rate with a high precision also in the original case of a nonzero correlation, as well as in the case of a dynamic correlation, when the correlation is modelled as a function of time. Finally, we use the algorithm to real market data and estimate the short rate before adoption of the euro currency in Slovakia, Estonia, Latvia and Lithuania.

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

“…A simple approximate solution of the bond pricing equation is useful in many applications, where an evaluation of the bond prices is necessary. We plan to focus our future work on using these approximations in inverse problems, similar to those in [24][25][26]. In particular, we are interested in estimating the implied correlation from the market data.…”

“…This implies that f ex (r d , r u , τ) = f ap (r d , r u , τ) + O(τ 3 ) and consequently, ∂ f ex /∂r = ∂ f ex /∂r + O(τ 3 ) for r = r d and r = r u . Using the orders of the functions D and U given by ( 22), we have the following estimates for the terms on the right hand side of (26): Recalling (23), we can, therefore, conclude that the right hand side of Equation ( 26) has the order O(τ 3 ), and the only O(τ 3 ) term comes from the expansion of the function h given by (24). Finally, it means that ω = 4 and…”

Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion

“…Ref. [Ste14] derived a Taylor expansion of the log of the bond prices in maturity T , see also [BSS17] for a survey. The approach was applied to several one-factor short rate models with constant coefficients, including the Dothan model.…”