G1 - General Financial MarketsReturn

The aim of this article is to complement the existing economic and financial strand of the literature by defining three alternative regimes of the clean price volatility of a bond with respect to the level of interest rates in the economy. The suggested method takes into account responses to the changing nature of financial markets and allows for the possibility of observing negative interest rates. Our approach enables to find particular values of switching points between alternative regimes. After showing main theoretical steps, an investigation of the dependence of such points on key parameters of bonds is provided. An empirical illustration follows, accompanied by a discussion of theoretical and practical effects of this bond property. This approach offers both theorists and interested practitioners a way of overcoming difficulties associated with computations because of the complicated theoretical background. The results can be generalised, so that they apply both to the life of a bond and to the behaviour of a portfolio of bonds at a point of time.

The choice of averaging method has considerable impact on the average yield of a financial variable. Usually, geometric average is preferred, though dissenting opinions exist. Here it is shown that the problem has a consistent solution, which is called the horizon-consistent average. It is shown why geometric and arithmetic average calculations are almost always biased. When using company valuation's most common SP500 dataset by Ibbotson Associates for 1928-2012 and the recommended 10-year forecasting horizon, consistent with the 10-year government securities in a CAPM model, the arithmetic average is severely flawed. On the other hand, the geometric average for similar horizons does not deviate much from the horizon-consistent average.

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model's parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model.