Sticky Continuous Processes have Consistent Price Systems

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni (2006).

Sticky Continuous Processes have Consistent Price Systems

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni (2006).

AN ALTERNATIVE INTEREST RATE TERM STRUCTURE MODEL

This paper proposes an alternative approach to the modeling of the interest rate term structure. It suggests that the total market price for risk is an important factor that has to be modeled carefully. The growth optimal portfolio, which is characterized by this factor, is used as reference unit or benchmark for obtaining a consistent price system. Benchmarked derivative prices are taken as conditional expectations of future benchmarked prices under the real world probability measure. The inverse of the squared total market price for risk is modeled as a square root process and shown to influence the medium and long term forward rates. With constant parameters and constant short rate the model already generates a hump shaped mean for the forward rate curve and other empirical features typically observed.