On character of points in the Higson corona of a metric space

We prove that for an unbounded metric space $X$, the minimal character $m\chi(\check X)$ of a point of the Higson corona $\check X$ of $X$ is equal to $\mathfrak u$ if $X$ has asymptotically isolated balls and to $\max\{\mathfrak u,\mathfrak d\}$ otherwise. This implies that under $\mathfrak u<\mathfrak d$ a metric space $X$ of bounded geometry is coarsely equivalent to the Cantor macro-cube 2^{<\IN} if and only if $\dim(\check X)=0$ and $m\chi(\check X)=\mathfrak d$. This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.Comment: 12 page

The Opinion Game: Stock price evolution from microscopic market modelling

We propose a class of Markovian agent based models for the time evolution of a share price in an interactive market. The models rely on a microscopic description of a market of buyers and sellers who change their opinion about the stock value in a stochastic way. The actual price is determined in realistic way by matching (clearing) offers until no further transactions can be performed. Some analytic results for a non-interacting model are presented. We also propose basic interaction mechanisms and show in simulations that these already reproduce certain particular features of prices in real stock markets.Comment: 14 pages, 5 figure

CDO and HAC

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on copula functions with up to three parameters, with default intensities estimated from market data and with a random loss given default that is correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. We apply hierarchical Archimedean copulae (HAC) whose construction allows for the fact that the risky assets of the CDO pool are chosen from six different industry sectors. The dependence among the assets from the same group is specified with the higher value of the copula parameter, otherwise the lower value of the parameter is ascribed. The copula with two and three parameters models the relation between the loss given default and the default times. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution.CDO, CDS, multivariate distributions, Copulae, correlation smile, loss given default

On the Systemic Nature of Weather Risk

Systemic weather risk is a major obstacle for the formation of private (non- subsidized) crop insurance. This paper explores the possibility of spatial diversification of insurance by estimating the joint occurrence of unfavorable weather conditions in different locations. For that purpose copula methods are employed that allow an adequate description of stochastic dependencies between multivariate random variables. The estimation procedure is applied to weather data in Germany. Our results indicate that indemnity payments based on temperature as well as on cumulative rainfall show strong stochastic dependence even at a national scale. Thus the possibility to reduce risk exposure by increasing the trading area of the insurance is limited. Irrespective of their economic implications our results pinpoint the necessity of a proper statistical modeling of the dependence structure of multivariate random variables. The usual approach of measuring stochastic dependence with linear correlation coefficients turned out to be questionable in the context of weather insurance as it may overestimate diversification effects considerably.weather risk, crop insurance, copula