Arrival Rate Functions

Abstract

Asset price dynamics are taken to be accumulations of surprise jumps in the logarithm of prices. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation. The motion is decomposed into a space dependent drift and a space dependent martingale component. Though there is some local mean reversion by and large the dynamics estimated is that of the momentum type. Risk compensation is seen by a linear relation between the exponential variation and measure distorted variations for the bid and ask prices of two price economies. Estimations are conducted for the S&P 500 index (SPX), the exchange traded fund for the financial sector (XLF), J. P. Morgan stock prices (JPM), the ratio of JPM to XLF and the ratio of XLF to SPX.

Keywords: Variance Gamma, Hunt Process, Markov Chain Approximation, Matrix Exponentiation, Momentum Function, Measure Distortion

JEL Classification: C13, C14, G1, G10, G12