2014/12/24 by Minh Man Ngo, Ngo, Minh Man, Huyen Pham +1
Economics, Econometrics and Finance · #49L25 #60G40 #FOS: Economics and business #Mathematical Finance (q-fin.MF) #msc:49L25 #msc:60G40 #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1412.7649
arxiv created 2014/12/24 · arxiv updated 2014/12/25
This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat position (no holding stocks), long one short the other and short one long the other. A fixed commission cost is charged with each transaction. We use a viscosity solutions approach to prove the existence and the explicit characterization of cut-off points via the resolution of quasi-algebraic equations. We illustrate our results by numerical simulations.