(a) Consider the following conditional mean process: y, = 0.1+e, where 11,4 0(0,0%) State whether the unconditional variance o of , is well defined for conditional variance processes (i) and (ii), respectively. If o is well defined, calculate its value. Show all necessary working. (i) o=0.095+0.58 (ii) o = 2.5+0.53 +0.47021 (b) For the following EGARCH process for the conditional variance of the return on a financial asset, explain the justification for the model, and from this justification state what sign you would expect y to have if there exists asymmetric effect of past shocks on future conditional variance. 8,-1 log o = +Blog o +r + a 0 04 (c) For the process in (i) of (a), assume Ex = 0 and calculate the forecast of the variance at h steps ahead of th, for h=1, 2 and steps. (d) Suppose that y, is the percentage return on a financial asset (i.e., y, = 1 is a 1% return). Suppose further that its conditional mean is modelled by the conditional mean process in (a) and its conditional variance is modelled by the conditional variance process in (i) of (a). At time T, produce a forecast of the probability of having a negative return at time T+1 assuming that the return at time T is zero. (a) Consider the following conditional mean process: y, = 0.1+e, where 11,4 0(0,0%) State whether the unconditional variance o of , is well defined for conditional variance processes (i) and (ii), respectively. If o is well defined, calculate its value. Show all necessary working. (i) o=0.095+0.58 (ii) o = 2.5+0.53 +0.47021 (b) For the following EGARCH process for the conditional variance of the return on a financial asset, explain the justification for the model, and from this justification state what sign you would expect y to have if there exists asymmetric effect of past shocks on future conditional variance. 8,-1 log o = +Blog o +r + a 0 04 (c) For the process in (i) of (a), assume Ex = 0 and calculate the forecast of the variance at h steps ahead of th, for h=1, 2 and steps. (d) Suppose that y, is the percentage return on a financial asset (i.e., y, = 1 is a 1% return). Suppose further that its conditional mean is modelled by the conditional mean process in (a) and its conditional variance is modelled by the conditional variance process in (i) of (a). At time T, produce a forecast of the probability of having a negative return at time T+1 assuming that the return at time T is zero