In this thesis, a factor model which estimates multivariate time series is extended to include an asymmetric relation between the returns of assets and the volatility of said assets. The model proposed in this thesis uses the classical factor model, with univariate logarithmic volatility equations to model the factors as well as the asset innovations. The volatility equations for the factors are extended to contain an asymmetric relationship with the factor returns of the day before. In this thesis, a method to estimate this asymmetric model is developed, the method of estimation mainly relies upon MCMC methods. A method to estimate the logarithmic likelihood for the model is provided as well. This method uses a particle filter to estimate the distribution of the volatility. Using the logarithmic likelihood, it is shown that the asymmetry in the data is identifiable, by comparing the likelihood of the model to the likelihood of the classical factor model, as well as to the likelihood of a factor model with a jump extension. Finally, the model is tested on a real data set of daily returns where its effectiveness is again compared to the classical model and the jump model.

In biological cells, information from the external environment of the cell is used to make survival related decisions. For these decisions, it is important that signals are accurately transduced from the outside to the inside of the cell. In \textit{Dictyostelium discoideum}, two opposing mechanisms using G-protein coupled receptors are used for this signalling: the precoupling mechanism, where second messenger molecules bind to the receptor before a ligand binds to it, and the collision coupling mechanism, in which the ligand binding comes first. In this paper, we investigated both models by analyzing how accurately they detect ligand bindings when different receptors are able to interact with each other. A similar analysis is done for returning messenger molecules. We found that the influence of receptors upon each other is low if the receptors operate under the same conditions. However, when the conditions are heterogeneous, the influence of receptors on each other is huge. The main reason for this influence is that ligand binding receptors which are more likely to get detected by messenger molecules will receive more of those messengers, because of their high diffusion rate. The effect of returning messenger molecules on the receptor signal was that ligand detection became possible at times where they otherwise would not be able to be detected anymore, given a replace rate which is low compared to the rate of binding and unbinding of a ligand to a receptor.