Pricing Physical Assets Internationally: A Non Linear Heteroskedastic Process for Equilibrium Real Exchange Rates

Transferring physical capital and transferring production and sales activities from one country to the other, typically entails large adjustment costs. The model of this paper features two homogeneous stocks of physical capital located in two different countries, separated by an "ocean." The two physical stocks are optimally invested in a random production process yielding real returns, or consumed by local residents, or transferred abroad. Retro-fitting, transferring and re-building capital equipment, and increasing production and sales abroad either takes time (during which capital is idle) or consumes real resources. Under proportional transfer costs, trade imbalances, consumption imbalances and capital imbalances between the two locations are shown to be persistent. The stochastic process for the deviation from the Law of One Price (LOP) is obtained. By construction, this process is compatible with financial market efficiency and with the possibility of (costly) trade in commodities. Whereas empirical studies have found no evidence against the hypothesis that LOP deviations follow a martingale, the theoretical process which is found differs markedly from a martingale: the drift is non linear and mean reverting. But the behavior of the conditional variance more than offsets the reverting effect of the drift and the conditional probability of a move away from Parity is greater than the probability of a move toward Parity. When some price barriers are reached, however, reversion is triggered. We decompose the real-interest rate differential into an expected price change and a risk premium for which a very simple expression is found. The behaviors over time of the rate differential and of its components are examined.