Asset Price Stability Analysis in Sparse Portfolios Under the Transactional Asset Pricing Approach

The Transactional Asset Pricing Approach (TAPA) is able to handle asset valuations on a portfolio level of size constrained markets against the backdrop of low liquidity hindering the estimation of the variance of returns. Prompted by a numerical simulation of the TAPA algorithm, we develop stability conditions associated with the valuation convergence for any maximal positive time period and positive number of assets. We present stability conditions at the local level, both in continuous and discrete algorithmic time, and we develop them by means of log-linearisation about the steady state of its equations’ variables. We conclude on the analytical existence of stability conditions at the local level up to four assets and any positive time period. We adduce analytical applications within such a region and present a solution for a benchmark calibration of the steady state parameters given two time periods and a single asset.