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

1. (a) Explain what is meant by the transition probability matrix of a homogeneous Markov chain. [5 marks] (b) Explain what is meant by the stationary distribution of a Markov chain? [5 marks] (c) A Markov chain has transition probability matrix, A, with entries Ouj; and stationary distribution . Write down an expression for the entries of the reverse Markov chain. [5 marks (d) Consider the following transition probability matrix of a homogo- neous Markov chain, with three states i,j and k (the TPM is in that order). If the stationary vector of the chain is (1/9, 2/9, 2/3), determine whether the Markov chain is reversible. 1 /0.2 0.2 0.6 0.1 0.6 0.3 4 \\0.1 0.1 0.8 [5 marks] (e) Let X1, X2, Xa be a sequence of random variables resulting from the above Markov chain. If X1 = i and Xs = j what is the probability that X2 = k? [5 marks]1. Consider the Markov chain with the following transition matrix. 0 0.5 0.5 0.5 0 0.5 0.5 0.5 0 (a) Draw the transition diagram of the Markov chain. (b) Is the Markov chain ergodic? Give a reason for your answer. (c) Compute the two step transition matrix of the Markov chain. (d) What is the state distribution *2 for t = 2 if the initial state distribution for t = 0 is no = (0.1, 0.5, 0.4) ?1. [9 marks] Answer the following, 9 multiple choice questions, Please select one answer for each question. You can also include your justification. This way, even though your answer is wrong, but you may receive 0.5 mark if your justification is reasonable. (1). Fill in the missing words to the quote: "Inferential statistical methods may be described as methods for drawing conclusions about based on computed from A. statistics, samples, populations B. populations, parameters, samples C. statistics, parameters, samples D. parameters, statistics, populations E. populations, statistics, samples