Volume 19, Issue 5

Plain vanilla options have a single underlying asset and a single condition on the payoff at the expiration date. For this class of options, a well known result of Duffie, Pan, and Singleton (Duffie, D., J. Pan, and K. Singleton. 2000. “Transform Analysis and Asset Pricing for Affine Jump-Diffusions.” Econometrica 68: 1343–1376. http://dx.doi.org/10.1111/1468-0262.00164.) shows how to invert the characteristic function to obtain a closed-form formula for their prices. However, multiple-asset and multiple-condition derivatives such as rainbow options cannot be priced within this framework. This paper provides an analytical solution for options whose payoffs depends on two or more conditions. We take the advantage of the inversion of the Fourier transform, resorting to neither Black and Scholes’s framework, nor the affine models’s settings. Numerical experiments based on the aforementioned class of derivatives are provided to illustrate the usefulness of the proposed approach.

Particle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

The aim of this paper is to empirically investigate the dynamic linkages between unemployment and shadow economy for 32 developing and developed countries for the period 1980–2009 using parametric and non-parametric techniques. To this end, the Hansen and Seo (2002) threshold cointegration approach and the nonlinear causality test of Kyrtsou and Labys (2006) are applied to assess these relationships. Results obtained clearly do not support the view that unemployment and shadow economy are neutral with respect to each other, except in the case of Bolivia, China, Colombia, Pakistan, Philippines and Portugal, where a neutral relationship is found. We find, however, considerable evidence of bi-directionality in Finland and Sweden. This indicates that high levels of unemployment lead to high levels of shadow economy and vice versa. We also find clear evidence of unidirectional causality running from unemployment to shadow economy in the US, Jamaica and Venezuela which implies that, in these three countries, a faster rate of unemployment promotes a higher share of the underground economy in total GDP. Further, the causality relationship appears to be uni-directional but reversed for Chile. Overall, our findings suggest that policy implications of the unemployment-shadow economy relationships should be interpreted with caution, taking into account the test-dependent and country-specific results.

The introduction of Euro currency was a game-changing event intended to induce convergence of Eurozone business cycles on the basis of greater monetary and fiscal integration. The benefit of participating into a common currency area exceeds the cost of losing autonomy in national monetary policy only in case of cycle co-movement. However, synchronization was put back mainly due to country-specific differences and asymmetries in terms of trade and fiscal policies that became profound at the outset of the global financial crisis. As opposed to previous studies that are mostly based on linear correlation or causality modeling, we utilize the cross-wavelet coherence measure to detect and identify the scale-dependent time-varying (de)synchronization effects amongst Eurozone and the broad Euro area business cycles before and after the financial crisis. Our results suggest that the enforcement of an active monetary policy by the ECB during crisis periods could provide an effective stabilization instrument for the entire Euro area. However, as dynamic patterns in the lead-lag relationships of the European economies are revealed, (de)synchronization varies across different frequency bands and time horizons.

In the paper we suggest the use of amplitude correlation coefficients (ACCs) and phase-locking values (PLVs) in examining business cycle synchronization. The quantities are calculated on the basis of instantaneous amplitudes and phase differences, which are computed here with the help of the non-decimated discrete analytic wavelet transform. We show that the coefficients constitute an interesting add-in to the statistical apparatus of examining business cycle synchronization. The PLVs correct the information provided by the coherency and correlation coefficients for the influence of amplitude changes and are of use in examining phase synchronization of business cycles, which is important in forecasting the effectiveness of a common monetary policy. By contrast, the ACCs are based solely on amplitude information and have the interpretation of phase-adjusted correlation coefficients, which can be used to evaluate stabilization policies or to forecast these policies’ effectiveness. The methodology is applied to examine cyclical synchronization of 20 European Union (EU) countries. We show, among other things, that during the run-up to the euro both amplitude and phase synchronization increased, with the former tending to change more rapidly. Furthermore, for the new EU members an EU effect is identified in both types of cyclical synchronization with the euro area.

We examine the causal relationship between crude oil and gold spot prices before and after the recent financial crisis. In the pre-crisis period, causality is linear and unidirectional, running from oil to gold. In the post-crisis period, a bidirectional nonlinear causality relationship emerges. Volatility spillover transpires as the source of nonlinearity during this period. The time path of the causal linkages both for the returns and the levels (cointegration) was assessed via dynamic bootstrap causality analysis. We find that the causal linkage from gold to oil is time dependent and that the non-Granger causality null hypothesis rejection rate increased considerably in the post-financial crisis period. The probability of gold Granger causing oil in the short-run increases by more than 30% during the recent financial and euro crisis.

We empirically investigate the link between monetary policy measures and stock market prices. We document the following stylized facts about stock market’s reaction to money supply and examine the effect across the entire distribution of stock returns. Using a nonparametric Granger causality in mean test, we find that money supply has no impact on stock prices, which confirms many of the existing results that were based on linear mean regression . By contrast, when a nonparametric causality in distribution (hereafter general Granger causality) test and quantile regression based test were used, the effect of money becomes apparent and statistically very significant. Interestingly, money supply affects the left and right tails of stock return distribution but not its center. This might indicate that the monetary policy measure money supply is effective only during recessions and expansions. We have also investigated the extent to which the impact of money supply on stock returns detected by the nonparametric and quantile regression based tests can be attributed to a time-varying conditional variance of stock returns. After controlling for volatility persistence in stock returns, we continue to find evidence for the reaction of conditional distribution of stock market returns to money supply growth rate.