(4) In finance, a zero coupon bond is a contract that pays out onedollar at maturity. The problem is how much money should onepay at time t to receive a dollar at time T? Here t < T and Tis the maturity of the bond. Different pricing models exist. Inthe Cox, Ingersoll and Ross (CIR) model, the price P(t,T,r)of a zero coupon bond at time t, maturing at T is given byP(t, T,r) = F(T – t,r;0) where F(t, r; X) satisfies the PDE-FOF+ (a – br)-OF1- - rF,%3Ddrsubject to F(0, r; X) = e-Ar. In this equation r represents the socalled spot rate of interest. To solve this, look for a solution ofthe form F(t,r; X) = e¬a$(t)-rý(t) and show that we must have2$(0) = 0, v(0) = X and1-v(t) = 50*v²(t) + bwý(t) – 1(0.1)d (t) = (t).(0.2)Solve the Riccati equation for and hence derive a formula forthe price of a zero coupon bond in the CIR framework. Theintegral to obtain ø from ý can be done in Mathematica.

F(t,r;λ)=e-aϕ(t)-rψ(t)F(0,r;λ)=e-λr=e-aϕ(0)-rψ(0)⇒ϕ(0)=0⇒ψ(0)=λ put F(t,r;λ) in given differential…

Answered: (4) In finance, a zero coupon bond is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A surfboard manufacturer lost $500,000 last year during a recession. Total revenue was $5,000,000 and total variable costs were 40% of sales. The production facility ran at 50% capacity. The production manager wants to know the following: a. What is the percent capacity required to break even? b. When the economy recovers this year, if the plant runs at 100% capacity what net income could the company realize? c. There is a possibility that sales could be so strong this year that the plant may be required to run at 120% capacity by offering a lot of overtime to its production workers. This would result in total variable costs rising by 35%. On a strictly financial basis, should the production manager plan to exceed capacity or should he advise top management to freeze production at 100% capacity? Justify your answer. Answer Solution- 9a. 58.3% 9b. $2,500,000 9c. $3,100,000
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Southland Corporation's decision to produce a new line of recreational products has resulted in the need to choose one of two automated manufacturing systems based on proposals from two vendors, A and B. The economics of this decision depends on the market reaction to the new product line. The possible long-run demand has been defined as low, medium, or high. Based on detailed financial analyses of system costs as a function of volume and sales under each demand scenario, the following payoff table gives the projected profits in millions of dollars. million. Decision Vendor A Vendor B million. Low $70 $160 Long-Run Demand Medium $150 $150 a. Determine the best decisions using the maximax, maximin, and opportunity loss decision criteria. Using the maximax criterion, choose -Select- Using the maximin criterion, choose -Select- To minimize the maximum opportunity loss, choose -Select- b. Assume that the best estimate of the probability of low long-run demand is 0.15, of medium long-run…
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