Abstract. The paper analyzes the regressive equation for cumulative excess returns with residual conditional variances as a GARCH(1,1) process and market uncertainty as an AR(1) Gaussian process with correlation parameter ρ. Under assumption that the lengths of the transaction time intervals are independent exponentially distributed random variables with sufficiently small mean h, we derive diffusion approximation equations. The continuous time limit equation allows concluding that a stationary conditional variance exists. Moreover, we derive this stationary distribution as inverse gamma distribution and discuss the dependence of this distribution on the correlation parameter ρ.
Keywords: diffusion approximation, volatility of excess returns, correlation of regression residuals.
Павленко Оксана Ивановна,
доктор математики, доцент Рижского технического университета, Латвия,
e-mail: Oksana.Pavlenko@rtu.lv.
Пола Айя,
магистр математики, преподаватель Рижского технического университета, Латвия,
e-mail: Aija.Pola@rtu.lv.
Царьков Евгений Фёдорович,
доктор физ.-мат. наук, профессор Рижского технического университета, Латвия,
e-mail: carkovs@latnet.lv; carkovs@livas.lv.