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 [Math. Finance 16(3), 569-582 (2006)].Comment: 10 pages, v3: incorporates minor corrections and the proof of the main result has been clarified, to appear in Journal of Applied Probabilit

Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility maximisation under transaction costs by establishing the existence of a so-called shadow price. This is a semimartingale price process, taking values in the bid ask spread, such that frictionless trading for that price process leads to the same optimal strategy and utility as the original problem under transaction costs. Our results combine arguments from convex duality with the stickiness condition introduced by P. Guasoni. They apply in particular to exponential utility and geometric fractional Brownian motion. In this case, the shadow price is an Ito process. As a consequence we obtain a rather surprising result on the pathwise behaviour of fractional Brownian motion: the trajectories may touch an Ito process in a one-sided manner without reflection.Comment: To appear in Annals of Applied Probability. We would like to thank Junjian Yang for careful reading of the manuscript and pointing out a mistake in an earlier versio

Sticky processes, local and true martingales

We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local martingale we may choose $Q$ arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present applications in mathematical finance

A pricing formula for delayed claims: Appreciating the past to value the future

We consider the valuation of contingent claims with delayed dynamics in a Black \& Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity

Sticky-price models and the natural rate hypothesis

A major criticism of standard specifications of price adjustment in models for monetary policy analysis is that they violate the natural rate hypothesis by allowing output to differ from potential in steady state. In this paper we estimate a dynamic optimizing business cycle model whose price-setting behavior satisfies the natural rate hypothesis. The price-adjustment specifications we consider are the sticky-information specification of Mankiw and Reis (2002) and the indexed contracts of Christiano, Eichenbaum, and Evans (2005). Our empirical estimates of the real side of the economy are similar whichever price adjustment specification is chosen. Consequently, the alternative model specifications deliver similar estimates of the U.S. output gap series, but the empirical behavior of the gap series differs substantially from standard gap estimates.Monetary policy ; Prices