3. Consider a one-period economy with two times, 0 and T. There are S N-3 securities...
No arbitrage pricing Consider the following two-period setting. There are 3 aseta A, B, C with respectivo payoffs EA, 1B, re while there are three possible future states w (1, 2, 3). Cuent asset prices are respectively A).Qac) 11/22 1 21/6 2a 3 1/3 2 21 Price in S 15 21 Construct risk-free bond in this cconomy and compute its price, following which compute risk free rate in this economy No arbitrage pricing Consider the following two-period setting. There are...
1. 30 points total] Consider the economy characterized with the following equations Y a-b(R- T), b> 0 IS relation Phillips TtTt-1 +vY+ o, v > 0 curve The economy has been in the long-run equilibrium up to period 0. In period 1, however, a one-time inflation shock o > 0 hits the economy. In other words, o > 0 in period 1 but o 0 in all other periods. (a) [10 points] The monetary policy rule (MPR) is given as...
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2, 3, 4, 5} has transition probability matrix P. ain {x. " 0) with state spare S-(0 i 2.3.45) I as transition proba- bility matrix 01-α 0 0 1/32/3-3 β/2 0 β/2 0 β/2 β/21/2 0001-γ 0 0 0 0 (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if...
2. Consider a two-period (T = 2) binomial model with initial stock price So = $8, u= 2, d=1/2, and “real world” up probability p=1/3. (a) Draw the binary tree illustrating the possible paths followed by the stock price process. (b) The sample space for this problem can be listed as N = {dd, jdu, ud, uu}. List the probabilities associated with the individual elements of the sample space 12. (c) List the events (i.e., the subsets of N2) making...
A Markov chain {Xn,n 2 0) with state space S 10, 1, 2,3, 4,5) has transition proba- bility matrix 0 1/32/3-ββ/2 01-α 0 β/2 0 0 0 0 0 0 β/2 β/21/2 0 1. Y (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if the states in each class are recurrent or transient and find their period (or determine that they are aperiodic)
Q5. Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, · · · } and transition matrix (pij ). Find (in terms QA for appropriate A) P{ max 0≤k≤n Xk ≤ m|X0 = i} . Q6. (Flexible Manufacturing System). Consider a machine which can produce three types of parts. Let Xn denote the state of the machine in the nth time period [n, n + 1) which takes values in {0, 1, 2, 3}. Here...
29&30 please 3 -23 4 3-2 25. 3 4926. |0 1 1 0 0-2 1 2-5 Finding a Basis In Exercises 27-30, find a basis B for the domain of T such that the matrix for T relative to B is diagonal. 27. T: R2→R-T(x, y) = (x + y, x + y) 28. T: R3→R, Tu, y, z) (-2x +2y -3z, 2r y -6z. 2y) a + (af+ 2b)s 29. T: Pi-Pi T(a + bx) 30. T: P㈠Pg Tle...
Consider an economy with two dates (t=0,1) and at t=1 there are three states. The following three stocks are traded: X1=(10,0,30) X2=(0,20,40) X3=(20,20,0) The t=0 prices of these stocks are given as follows (P1, P2, P3)=(12, 14, 8). (a) Is there an arbitrage? Suppose an investment firm sells options. (b) What is the t=0 price (premium) of a call option on stock 2 with exercise price E=10? (c) What is the t=0 price (premium) of a put option on stock...
The periodic function so(t) with period 16 given by so(t) = 0 1 10 if – 8<t< -1 if –1<t<1 if 1 <t<8. has the Fourier series defined by S.(0) = 0.125 and for n +0 So(n) = 0.125 * sin(n72/16) 772/16 Use linearity and the shifting property to find the Fourier Series for s(t), defined by s(t) = O 1-5 4 lo if – 8<t<1 if i<t<3 if 3 <t<5 if 5 <t<8. S(0) = and for n 70...
Help with any of these? Practice Problems 31 n* cos n 12 23. Σ㈠)"21/" 32n-1 n(ln n)3 n-2 24 + 5 -1 In n 25, Σ(-1)" 15 35 та і 36 (2n)" 16 26 17. Σ5n3nn Σ-π)" 7. k 27, 37 n-I E1 28. +1 10 k + 5 18 19 39 2.5.8(3n + 2)T ㄒㄧ- Σ(阪-1) 10 30 40 8m - 5 '고 (n + 1) (n-2) Practice Problems 31 n* cos n 12 23. Σ㈠)"21/" 32n-1 n(ln n)3...