QUESTION 3: (25 marks) Identify, explain briefly (in 2 sentences maximum for each) and specify the general equation for each of the following multivariate time series and volatility models: a. VAR(p) model b. Granger causality model c. VEC model d. ARDL model a. GARCH(p, q) model b. GARCH-M c. EGARCH d. State the basic difference between ARCH-GARCH models and stochastic volatility models in financial econometrics. e. What is the most popular technique in modelling long-run relationships in finance? 3)The Black-Karasinski model of stochastic interest rate r is given by stochastic differential equation (SDE) drer A A+ B - C'In ri) dt + BrdWi where W, is a Wiener process and A, B and C are constants. a) Use H = Inr, to get a new SDE via Ito's formula.b) Make use of Geometric Brownian Motion to obtain H. c) find the interest rate r, as a function of AdW.. 3. Ito's Lemma (Univariate Case) and Ito's Calculas. In the risk-neutral world, the stock price is modeled as: ds, = rs.dt+S.dB where Be is a standard Brownian motion under the risk-neutral measure Q. 1). Please derive the stochastic differential equation for F = S,e"(7-1); 2). Please derive the stochastic differential equation for f = S, +2t; 3). Please derive the functional form of the stock price S, in the risk-neutral world.