Risk Minimization for a Filtering Micromovement Model of Asset Price

Abstract

The classical option hedging problems have mostly been studied under continuous-time or equally spaced discrete-time models, which ignore two important components in the actual price: random trading times and market microstructure noise. In this paper, we study optimal hedging strategies for European derivatives based on a filtering micromovement model of asset prices with the two commonly ignored characteristics. We employ the local risk-minimization criterion to develop optimal hedging strategies under full information. Then, we project the hedging strategies on the observed information to obtain hedging strategies under partial information. Furthermore, we develop a related nonlinear filtering technique under the minimal martingale measure for the computation of such hedging strategies.Risk minimization, Minimal martingale measure, Filtering, Counting process, High frequency data,

A branching particle approximation to a filtering micromovement model of asset price

“…Moreover, the filter developed can be used to estimate locally risk-minimizing hedging strategy for FM models derived in Lee and Zeng (2010) and the optimal trading strategy for mean-variance portfolio selection problem of the FM models derived in Xiong and Zeng (2011).…”