DVA for Assets

The effect of self-default on the valuation of liabilities and derivatives (DVA) has been widely discussed but the effect on assets has not received similar attention. Any asset whose value depends on the status, or existence, of the firm will have a DVA. We extend (Burgard and Kjaer 2011) to provide a hedging strategy for such assets and provide an in-depth example from the balance sheet (Goodwill). We calibrate our model to seven US banks over the crisis period of mid-2007 to 2011. This suggests that their reported profits would have changed significantly if DVA on assets, as well as liabilities, was included - unless the DVA was hedged.Comment: 16 pages, 4 figure

The asymptotic determinant of the discrete Laplacian

We compute the asymptotic determinant of the discrete Laplacian on a simply-connected rectilinear region in R^2. As an application of this result, we prove that the growth exponent of the loop-erased random walk in Z^2 is 5/4.Comment: 36 pages, 4 figures, to appear in Acta Mathematic

Local statistics of lattice dimers

We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of maximal entropy $\mu$ on the space of tilings of the plane with dominos. We construct a measure $\nu$ on the set of lozenge tilings of the plane, show that its entropy is the topological entropy, and compute explicitly the $\nu$-measures of cylinder sets. As applications of these results, we prove that the translation action is strongly mixing for $\mu$ and $\nu$, and compute the rate of convergence to mixing (the correlation between distant events). For the measure $\nu$ we compute the variance of the height function.Comment: 27 pages, 6 figure