Homework #2 Due Tuesday, February 1, 2022 Consider two Ito processes dX (t) = Hx(t) dt + ox(t) dBx(t), dY (t) = My(t) dt + oy(t) dBy(t) , where By and By are Brownian motions with correlation coefficient process p. 1. Show that if Z = XY, then What are the drift and quadratic variation of Z? 2. Show that if Z = Y/X, then dz dy dx Z Y X- What are the drift and quadratic variation of Z? 3. Show that if Z = ed, then = dx + . (dx)z What are the drift and quadratic variation of Z? 4. Show that if Z = log X, then dx dZ = What are the drift and quadratic variation of Z? 5. Show that if Z = e fo q(s)ds x, then - = q dt + . What are the drift and quadratic variation of Z