Ali Company and Bill Company entered into a semi-annual pay plain vanilla interest rate swap with a nominal value of $8,000,000. Bill offered to pay Ali a fixed annual rate of 2.75% (with semi-annual compounding). The remaining life of the swap is nine months. Assume the six-month LIBOR rate observed three months ago was 2.6% with semi-annual compounding. Today's three and nine month LIBOR rates are 2.526% and 2.846% (with continuous compounding). The implied forward rate is 3.0287% with semi-annual compounding. What is the value of the swap to Bill Company using the FRA methodology? Do not round intermediate calculations.

A.$4,950

B.$2,009

C.-$1,407

D.$5,613

Ali Company and Bill Company entered into a semi-annual pay plain vanilla interest rate swap with a nominal value of $8,000,000. Bill offered to pay Ali a fixed annual rate of 2.75% (with semi-annual compounding). The remaining life of the swap is nine months. Assume the six-month LIBOR rate observed three months ago was 2.6% with semi-annual compounding. Today's three and nine month LIBOR rates are 2.526% and 2.846% (with continuous compounding). The implied forward rate is 3.0287% with semi-annual compounding. What is the present value of the net cash flow (or payoff) at nine months point to Bill Company?

A.$4,556

B.$4,913

C.$8,904

D.$10,913

Consider a Markov chain {Xn, n = 0, 1, . .. } on the state space S = {0, 1, 2}. Suppose that the Markov chain has the transition matrix 0 1 - P = 1 0 0 N/H 1. Show that the state space is irreducible. 2. Show that the Markov chain is periodic. Find the period of the Markov chain. 3. Let h denote a stationary mass of the Markov chain. Find h(x) for all x E S.4. Consider a discrete-time Markov chain with the following probability transition matrix 0 0 0 0 7 1-3-y P = 1-I-VVO T 0 0 1 0 Is it possible to choose values for a and y so that the Markov chain has the following properties? In each case, state the values of a and y, or give a brief reason why it is not possible. (a) The Markov chain has period 2. [2) (b) The Markov chain is reducible. (c) The Markov chain has at least one transient state. UNN (d) The Markov chain has invariant distribution (1/4, 1/4, 1/4, 1/4).2. Markov chain transitions P = [P/j] = Al- AI- NI- Al- NI- AI- NI- AI- Al- Let X1 be distributed uniformly over the states {0, 1, 2}. Let (Xill be a Markov chain with transition matrix P; thus, P(Xn+1=j \\Xn= i) = Pu , i, j E {0, 1, 2}. (a) Is the information source stationary? ~ (b) Find the stationary distribution of the Markov chain (c) Find the entropy rate of the Markov chain