E47 - Money and Interest Rates: Forecasting and Simulation: Models and ApplicationsReturn

We estimate a financial stress index for the Czech Republic and examine its development during the 2002-2014 period. We find a marked increase in financial stress at the beginning of the global financial crisis with a decrease to nearly pre-crisis levels by the end of our study period. Next, we estimate vector autoregression models of the Czech economy and find that financial stress has systematic effects on output, prices and interest rates, with the maximum response occurring approximately one and a half years after the shock. Specifically, an increase in financial stress is associated with higher unemployment, lower prices and lower interest rates, indicating its detrimental effects on the real economy.

This paper examines the theoretical concept of equilibrium in the money market that is empirically verified for the economy of the Czech Republic. The subject of the analysis is the relationship defining equilibrium in the domestic money market, i.e. when money demand corresponds to the money supply in the economy. The main objective is to determine whether such a long-term equilibrium relationship exists by verifying this assumption on real data for the Czech economy. The Johansen cointegration approach is applied for modelling the money demand function including four domestic macroeconomic indicators: money supply, price level, gross domestic product, and interest rate. The results suggest that the level of real money supply fluctuated around the estimated long-run equilibrium value in the analysed period 2000-2013.

The aim of our paper is to formulate and empirically verify the simple backward looking econometric model of the monetary policy rule, which would be able to describe the development of monetary policy rate, namely only on the basis of statistically measured and at the given time available information. We focus on the Czech National Bank, the National Bank of Poland and the Magyar Nemzeti Bank in the period of January 1999 to April 2012. In the present paper we discuss some methodological problems associated with the ex-post empirical verification of the central bank's monetary policy rule. We construct an empirical model of the monetary policy rule, justify the choice and the inclusion of explanatory variables, analyse the statistical properties of time series, and verify the alternative forms of econometric models. Our analysis showed that the development of monetary policy rate in the reporting period can be explained by the past and present development of four explanatory variables: yearly inflation rate, exchange rate, ECB main refinancing rate and growth rate of M2. The annualized inflation rate proved to be statistically insignificant in the model. We find interesting that the statistical quality of the estimated model was further increased after a six-month lag of the annual inflation rate added to the model.

In case that a central bank is withdrawing excess liquidity, there arises a question whether the monetary policy based on repo operations (withdrawal repo) is identically efficient as the monetary policy relying on repo rate connected with reverse repo (issuance repo) when central banks provide liquidity. The analysis of this problem is a main subject of the article. Authors develop microeconomic model of commercial bank behaviour, which is used for the definition of conditions when the interest rate policy of central bank based alternatively on repo rates for repo and reverse repo operations is efficient. Statistical data (time series of 1998 - 2011, monthly data frequency) are analysed and econometric verification of alternative forms of econometric models is performed. The authors arrived at a conclusion that the Czech National Bank's monetary policy operating in conditions of excess liquidity withdrawal through repo operations is efficient. In case of the Czech Republic an increase in repo rate on withdrawal repo should lead to an increase in interest rates of commercial banks and to a reduction in the credit activity of commercial banks and hence to the successful implementation of Czech National Bank's restrictive monetary policy.

The paper presents both the theoretical account of the issue of foreign exchange risk premium and the actual estimates of the time-varying risk premium for the cases of the Czech koruna to euro and US dollar. The risk premium is modelled within a state space framework and estimated using the Kalman filtering procedure. Some financial market fundamentals are used to estimate the risk premium, and thus not only do the estimates give insight into the foreign exchange market behaviour but also into some linkages between the various segments of the financial market as a whole.

We investigate valuation of derivatives with payoff deined as a nonlinear though close to linear function of tradable underlying assets. Interest rate derivatives involving Libor or swap rates in arrears, i.e. rates paid at wrong time, are a typical example. It is generally tempting to replace the future unknown interest rates with the forward rates. We show rigorously that indeed this is not possible in the case of Libor or swap rates in arrears. We introduce formally the notion of linear plain vanilla derivatives as those that can be replicated by a inite set of elementary operations and show that derivatives involving the rates in arrears are not (linear) plain vanilla. We also study the issue of valuation of such derivatives. Beside the popular convexity adjustment formula, we develop an improved two or more variable adjustment formula applicable in particular on swap rates in arrears. Finally, we get a precise fully analytical formula based on the usual assumption of log-normality of the relevant tradable underlying assets applicable to a wide class of convexity related derivatives. We illustrate the techniques and different results on a case study of a real life controversial exotic swap.