Constructing the binomial interest rate tree, Financial Management

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%

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

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
Related Questions
What is the investment opportunity schedule (IOS)?  How does it help financial managers make business decisions? The investment opportunity schedule illustrates graphically pro

Q. Formulation of Collection Policy ? Formulation of Collection Policy:- The third characteristic of the receivable management is to formulate a collection policy. Collection p

A factoring company has offered a one-year agreement with Glub Ltd to both manage its debtors and advanced 80 per cent of the value of all its invoices immediately a sale is invoi

Q. Demerits of net present value method? (i) Difficult to Understand as well as Implement:- This method is tricky to understand as well as implement in comparison to the paybac

Offshore Financial Center It is a location with banking facilities to accept deposits and make loans in currencies various from the currency's country of origin. Banks located

a) Gross profit shows the difference between a firm's sales revenues and its direct cost of sales (COGS). Net profit, however, is calculated after deducting overheads (expenses) fr

Q. Computation of Value of the Firm? Illustration:- EBIT                                                               = 50,000 10% Debentures

Q. Explain Rate of the stock turnover? Rate of the stock turnover: this is high degree of the inverse co relation between the quantum of the working capital requirement and the

Q. Show Gross Vs net working capital? The distinction between the gross working capital or the net working capital does not in any way undermine the relevance of the concepts o

Short-term funds having a maturity of 15 days and over are categorized as term money. Banks access this term money route to bring greater stability in their short