Consider a portfolio P(t) of $10 million invested with the following weights and assets: IBM stock 40%, 10-year Treasury Bill 30%, and Chinese Yuan 30%. You are given the following assumptions on the dynamics of each asset in terms of SDEs: For IBM dX, = 0.01X_dt +0.3W, Xo = 80 For a Unit of T-Bill dy; = 100(90000 + 1000t - Y,)dt + VYdW, Yo = 90000 dZ = 5(6 - 2.) +0.01 Zd, 20 = 6.1 1. Calculate the number of shares and amount of Yuan in P(0) at the initial time t = 0. 2. For simplicity, suppose that the Wiener (Brownian) motions in the three processes are independent and perform a Monte-Carlo simulation for all assets for ten days, i.e. t = 2. Use 3 million simulations with At = 0.001. 3. Calculate the 10-day value-at-risk VaR and the conditional value-at-risk CVR of the portfolio. Consider a portfolio P(t) of $10 million invested with the following weights and assets: IBM stock 40%, 10-year Treasury Bill 30%, and Chinese Yuan 30%. You are given the following assumptions on the dynamics of each asset in terms of SDEs: For IBM dX, = 0.01X_dt +0.3W, Xo = 80 For a Unit of T-Bill dy; = 100(90000 + 1000t - Y,)dt + VYdW, Yo = 90000 dZ = 5(6 - 2.) +0.01 Zd, 20 = 6.1 1. Calculate the number of shares and amount of Yuan in P(0) at the initial time t = 0. 2. For simplicity, suppose that the Wiener (Brownian) motions in the three processes are independent and perform a Monte-Carlo simulation for all assets for ten days, i.e. t = 2. Use 3 million simulations with At = 0.001. 3. Calculate the 10-day value-at-risk VaR and the conditional value-at-risk CVR of the portfolio