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 r_1,L at the node T_L 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 r_1,L is in line with the 2-year on-the-run issue.

In similar manner, rates are determined for year-two - r_2,LL, r_2,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 (r_1,L and r_1,H).

A guess is made of the value r_2,LL, and based on the formula discussed earlier in this chapter, the 

value of r_2,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

Assumed Volatility = 10%

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

 

Assumed Volatility = 10%

Coupon tate = 5%

Posted Date: 9/10/2012 6:51:49 AM | Location : United States

Ask an Expert

Related Discussions:- Constructing the binomial interest rate tree, Assignment Help, Ask Question on Constructing the binomial interest rate tree, Get Answer, Expert's Help, Constructing the binomial interest rate tree Discussions

Write discussion on Constructing the binomial interest rate tree
Your posts are moderated

Write your message here..

Related Questions

Homework, Assume Main Street Store’s Net Sales in 2010 were $1,000,000 and ... Assume Main Street Store’s Net Sales in 2010 were $1,000,000 and it’s Net Income in 2010 was $17,000. Thus, between 2010 and 2011 Main Street Store’s net sales increased 20%. Durin

Debt ratio, Calculate the sustainable growth rate Calculate the sustainable growth rate

Standard communication protocol used for the internet, Question: (a) W... Question: (a) What is a computer virus? List and explain the different type of computer viruses? (b) List 4 steps which you can use to minimize the chances of being infec

What is a digital certificate, QUESTION (a) Describe briefly the main s... QUESTION (a) Describe briefly the main security measures to protect E-Banking systems and ensure secure E-Banking transactions. (b) (i) What is a digital certificate? (ii

Valuing an option-free bond, To value an option-free bond, we must de... To value an option-free bond, we must determine the on-the-run yield curve for the particular issuer whose bond we have to value. This on-the-run yield curve used

Determine the important ways of financing, Determine the important ways of ... Determine the important ways of financing Financing could be by two ways: debt (loans from different sources such as financial institutions, banks,public etc.) and equity (capi

Effective use of focused marketing, a) A niche market refers to a lucrative... a) A niche market refers to a lucrative and small market segment. Marketing strategy is targeted and concentrated at this specific market segment. Pink Ladies are specifically targ

Operational cycle, using the operating cycle and any other financial manage... using the operating cycle and any other financial management knoweledge,dicuss the applicability of such a cycle to the poultry biussiness in uganda (consider broilers)

Financial position as assets, One of the well-known soccer clubs in Austral... One of the well-known soccer clubs in Australia, Sydney, has made a decision to include its players on the club's statement of financial position as assets. These players are signe

Explain opportunity costs affect the capital budgeting, How do opportunity ... How do opportunity costs affect the capital budgeting decision-making process? Opportunity costs imitate the foregone benefits of the alternative not chosen while a capital budge