A characteristic function-based method is proposed to estimate the time-changed Lévy models, which take into account both stochastic volatility and infinite-activity jumps. The method facilitates computation and overcomes problems related to the discretization error and to the non-tractable...

This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator...

In a general, finite-dimensional securities market model with bid-ask spreads, we characterize absence of arbitrage opportunities both by linear programming and in terms of martingales. We first show that absence of arbitrage is equivalent to the existence of solutions to the linear programming...