Constructing the binomial interest rate tree, Financial Management

Assignment Help:

The fundamental principle is that when a tree is used to value an on-the-run issue, the resulting value should be arbitrage free i.e., it should be equal to the observed market value. Also, the interest rate tree should be consistent with the assumed interest rate volatility.

Let us, with help of an example, look at the process of constructing an interest rate tree:

The interest rate at the first node T would be the current 1-year on-the-run issue rate. The interest rate for year-one would be calculated using the coupon rate for the 2-year on-the-run issue, assumed interest rate volatility, and the interest rate at the base of the tree. Given these, the interest rates are determined on a trial and error basis. First, the lower rate r1,L at the node TL is assume and then using the formula (discussed earlier in this chapter) the interest rate at the higher value is calculated. It is then compared with the 2-year on-the-run issue to see if there are discrepancies in both the values; it implies that the assumption made is incorrect. If the value is too high, a higher rate guess should be made and if the value is too low a lower rate guess is to be made until the value of r1,L is in line with the 2-year on-the-run issue.

In similar manner, rates are determined for year-two - r2,LL, r2,HL and r 2,HH. The information required for this task includes:

  1. The coupon rate for the 3-year on-the-run issue.

  2. Assumed interest rate volatility.

  3. The interest rate at the base of the tree.

  4. The two 1-year rates (r1,L and r1,H).

A guess is made of the value r2,LL, and based on the formula discussed earlier in this chapter, the 

value of r2,HL and r 2,HH are calculated. If the value generated by this process is not equal to the market value of the 3-year on-the-run issue, the process is to be repeated again. An iterative process is again followed. Table 2 shows the binomial interest rate tree for the issuer for valuing issues up to four years of maturity assumption volatility for the 1-year rate of 10% and Table 2 verifies that the rates on the binomial interest rate tree are the correct values. This is arrived at by showing that when the 3-year on-the-run issue is valued using backward induction method the value is 100, which is nothing but the market value of the 3-year on-the-run issue.

Table 2: Binomial Interest Rate Tree

355_binomial interest rate tree1.png

Assumed Volatility = 10%

Table 2: Verification of the Rates on the Binomial Interest Rate Tree

638_binomial interest rate tree.png

 

Assumed Volatility = 10%

Coupon tate = 5%


Related Discussions:- Constructing the binomial interest rate tree

Validity of the accounting implications, Question: In each case below a...

Question: In each case below and having regard to your knowledge of Accounting Concepts, comment on and assess the validity of the accounting implications/practices to be adop

Explainthe principles of banking and finance, An introduction to the princi...

An introduction to the principles of banking and finance It covers a broad variety of topics using an economic perspective and aims to give a general background to any student

Bonds, Explain what a bond is and discuss its nature as a "fi xed income" s...

Explain what a bond is and discuss its nature as a "fi xed income" security.Discuss important terms in relation to bonds as the "price", "maturity", "current yield", "yield to matu

Explain safe harbour rule, Q. Explain Safe Harbour Rule? Safe Harbour R...

Q. Explain Safe Harbour Rule? Safe Harbour Rule - Concept in statutes and regulations whereby a person who meets listed requirements would be preserved from adverse legal actio

Explain briefly the term e-billing, QUESTION (a) Describe briefly three...

QUESTION (a) Describe briefly three methods of electronic payment. (b) (i) Explain briefly the term E-Billing. (ii) Outline three advantages of E-Billing. (c) Why is c

Determine the factors which common stockholders consider, What are some of ...

What are some of the factors which common stockholders consider while deciding how much, if any, cash dividends they desire from the corporation in which they have invested? Comm

Determine the key factor affecting financing costs, Determine The key facto...

Determine The key factor affecting financing Costs Because cost of capital is measured under the assumption that both firm's asset structure and its capital (financial) structu

Cost of retained earnings , Cost of Retained earnings (K ) Retained ea...

Cost of Retained earnings (K ) Retained earnings are that portion of EPS that is retained by the firm.  This may be measured as the rate of return which the existing share hol

A/a2, A/A2 is generally the second- or third-highest rating that a rating a...

A/A2 is generally the second- or third-highest rating that a rating agency gives to a security or carrier. This rating indicates that there is a comparatively low risk of default a

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd