This paper introduces asymmetric impulse response functions and asymmetric variance decompositions. It is shown how the underlying variables can be transformed into cumulative positive and negative changes in order to estimate the impulses to an asymmetric innovation. An application is provided...

The minimum variance hedge ratio is widely used by investors to immunize against the price risk. This hedge ratio is usually assumed to be constant across time by practitioners, which might be too restrictive assumption because the optimal hedge ratio might vary across time. In this paper we put...

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the unconditional volatility of the original asset is increasing during...

Since the seminal work by Engle (1982), the autoregressive conditional heteroscedasticity (ARCH) model has been an important tool for estimating the time-varying volatility as a measure of risk. Numerous extensions of this model have been put forward in the literature. The current paper offers...

One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This asumption can be fulfilled only in perfectly liquid markets. Since most markets are illqiud, this asumption might be too...

Tests for conducting asymmetric Granger causality within a panel system are introduced in this paper. It is shown how the cumulative sums of negative and positive shocks can be constructed to investigate whether the potential causal effects of these shocks are asymmetrical or not within a panel...