Asset pricing with general transaction costs: Theory and numerics

Abstract

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts-the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known well-posedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen, and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.

Simulation analysis of asset pricing based on the Gaussian process

“…The evolution and development of asset pricing theories and models have irreplaceably influenced macroeconomic operations and decisions and have substantially affected investors' investment strategies and the operation of capital markets [1]- [2]. Asset pricing theories have been divided into two categories depending on the assumed contextual framework: asset pricing theories of rational expectations and asset pricing theories of irrational expectations [3]. The former implicitly assumes that there are rational investors in the market who make rational investment decisions based on market changes, that asset prices fluctuate around fundamentals, and that whenever asset prices deviate from fundamentals, the market has a mechanism to automatically adjust them back to fundamentals [4]- [5] The latter implies that there are irrational investors in the market who may be "herding" or "overvolatile" that market fundamentals no longer determine asset prices and that there are behavioral biases, market frictions, and even mispricing in the market that lead to asset price bubbles [6]- [7].…”