Johan Walden

Asset Pricing in Large Information Networks

We study asset pricing in economies with large information networks. We focus on networks that are sparse and have power law degree distributions, in line with empirical studies of large scale social networks. Our theoretical framework yields a rich set of novel asset pricing implications. We derive closed form expressions for price, volatility, profitability and trading volume, as functions of the network topology. We also study agent welfare and show that the network that optimizes total welfare is typically a uniform one with an intermediate degree of connectedness.

On the approximation of singular source terms in differential equations

We study differential equations with singular source terms. For such equations classical convergence results do not apply, as these rely on the regularity of the solution and the source terms. We study some elliptic and parabolic problems numerically and theoretically, and show that, with the right approximation of the singular source terms, full convergence order can be achieved away from the singularities, whereas the convergence will be poor in a vicinity of these.

Hedging Labor Income Risk

We use a detailed panel data set of Swedish households to investigate the relation between their labor income risk and financial investment decisions. In particular, we relate changes in wage volatility to changes in the portfolio holdings for households that switched industries between 1999 and 2002. We find that households do adjust their portfolio holdings when switching jobs, which is consistent with the idea that households hedge their human capital risk in the stock market. The results are statistically and economically significant. A household going from an industry with low wage volatility to one with high volatility ceteris paribus decreases its portfolio share of risky assets by up to 35%, or

Estimating Time and Size of Bioterror Attack

15,575.

Filter Bank Methods for Hyperbolic PDEs

Time and size of possible bioterror event estimated in real time.

BENCHOP – The BENCHmarking project in option pricing

We use biorthogonal filter banks to solve hyperbolic PDEs adaptively with a sparse multilevel representation of the solution. The methods described are of finite difference type, and the filter banks are used to give a sparse representation of signals and to transform between grids on different scales. We derive bounds for the error and number of coefficients in the sparse representation. These bounds also apply for filter banks that are not associated with any wavelets. We develop algorithms for fast differentiation and multiplication in detail. The strength of the method is shown in various test problems.

Analysis of the direct Fourier method for computer tomography

The aim of the BENCHOP project is to provide the finance community with a common suite of benchmark problems for option pricing. We provide a detailed description of the six benchmark problems together with methods to compute reference solutions. We have implemented fifteen different numerical methods for these problems, and compare their relative performance. All implementations are available on line and can be used for future development and comparisons.

Heavy-tailed distributions and robustness in economics and finance

The authors develop a direct Fourier method (DFM) for reconstructing a function from its X-ray projections. They introduce a framework that can be used to get a quantitative comparison between different choices of basis functions in the step of resampling from polar to Cartesian coordinates. They use the framework to compare polynomial interpolation, approximated sinc-functions, Gaussians, splines, and Kaiser-Bessel functions. The resulting algorithm is very fast, requiring 12.5 N/sup 2/ log, N+49 N/sup 2/ flops. Numerical experiments show it to be efficient.

Recovery with Unbounded Diffusion Processes

Introduction.- Implications of Heavy-tailed ness.- Inference and Empirical Examples.- Conclusion.

Trading, Profits, and Volatility in a Dynamic Information Network Model

We analyze the problem of recovering the pricing kernel and real probability distribution from observed option prices, when the state variable is an unbounded diffusion process. We derive necessary and sufficient conditions for recovery. In the general case, these conditions depend on the properties of the diffusion process, but not on the pricing kernel. We also show that the same conditions determine whether recovery works in practice, when the continuous problem is approximated on a bounded or discrete domain without further specification of boundary conditions. Altogether, our results suggest that recovery is possible for many interesting diffusion processes on unbounded domains.