Binomial model, Financial Management

Assignment Help:

The option features embedded in many bonds and fixed-income securities have made the binomial interest rate tree approach a valuable model for pricing debt. Binomial model is an option valuation method developed by Cox, Ross, Rubinstein and Sharpe in 1979. This method of pricing options or other equity derivatives is based on the assumption that probability of each possible price follows a binomial distribution and that prices can either move to a higher level or a lower level with time until the option expires.

To value bonds using the binomial model, a binomial interest rate tree is to be constructed first. A binomial interest rate tree is nothing but a graphical representation of the short-term interest rates over a period of time based on some assumption about interest rate volatility. In this tree, each node represents a defined time period, say one year. Each node is represented by the letter T. The current year spot rate for the specified time period, in our example one-year spot rate, is represented by r0. As the model is based on the assumption that each possible price can either move higher or lower, each node gives rise to two options, TH and TL, where H represents higher and L represents lower. (Multiple paths to same node have been avoided to keep the figure simple. For example, HL can be reached in two ways, HL and LH, but only HL is shown in the Table.)

In Table 1, we see that T is the starting point of the interest rate tree, and r0 represents the current 1-year spot rate. It is assumed that the 1-year rate can take two possible values, either higher or lower, in the defined time period, i.e., 1-year in our example and they both have the same probability of occurrence.

         σ       = Assumed volatility of the 1-year rate.

         r1, L      = The lower 1-year rate one year from now.

         r1, H      = The higher 1-year rate one year from now.

Table 1: Binomial Interest Rate Tree

1634_binomial model.png

Now, we can define the relationship between the lower and higher value as follows:

r1, H = r1, L ( e )

e is the base of the natural logarithm, 2.71828.

Let us calculate the values using a hypothetical example; let us assume that the value of r1, L to be 4.7801, σ is 10% per year, then,

r1, H = 4.7801% (e 2*0.10) = 5.8384

In the second year, we find three possible values for the one year rate; they are:

r2, HH  =      1-year rate in second year assuming the higher rate in the first year and the

 higher rate in the second year.

r2, HL   =       1-year rate in second year assuming the higher rate in the first year and the

 lower rate in the second year.

r2, LL    =       1-year rate in second year assuming lower rate in first year and lower rate in

 second year.

r2, HH  is defined as r2, LL (e 4 σ) and r2, HL = r2, LL( e ).

Assuming r2, LL to be 4.8051% and σ as 10%, we can determine r2, HH, r2, HL as follows:

r2, HH = 4.8051% (e 4*0.10) = 7.1683%

r2, HL = 4.8051% (e 2*0.10) = 5.8689%

There are four possible values for the 1-year rate in the third year, they are denoted as r3, HHH, r3, HHL , r3, HLL and r3, LLL.

The relationship between them can be expressed as follows:

r3, HHH = r3, LLL( e )

r3, HHL = r3, LLL(e )

r3, HLL = r3, LLL( e ).

Let us make the Table easier to understand by replacing the notations with the simplified notations.

Table 2: Binomial Interest Rate Tree with One-Year Rates

1897_binomial model1.png

*rt equals forward 1-year lower rate. t year from now.

In valuing option free bonds, we have seen the use of single forward rate, but in valuing bonds with embedded option we use a set of forward rates, as at every level we come with more then one option.


Related Discussions:- Binomial model

Define leverage, Q. Define leverage? Meaning of Leverage: - The diction...

Q. Define leverage? Meaning of Leverage: - The dictionary significance of the term leverage refers to 'an increased means of accomplishing some purpose'. For instance leverage

What do you mean by credit policy, Q. What do you mean by Credit policy? ...

Q. What do you mean by Credit policy? Credit policy: the credit policy of the concern in its dealing with the debtors and the creditors influencly consider the requirement of t

Determine what is current ratio - position ratios, Determine Current ratio...

Determine Current ratio  or working capital ratio CA = Current assets/Current liabilities (times) Current ratio measures the short term solvency or liquidity; it demonstra

Calculate the new interest rate and excel function pv, Continuing growth of...

Continuing growth of the company has required that we issue the company''s corporate debt soon. As you know, in 6 months we plan to issue $10 million worth of 20-year corporate bon

Waht are additional information required in chromex plc, Additional informa...

Additional information required Specification of a time scale for the evaluation. Predict cash flow details year by year for period specified in the time scale. An approxima

Financial institution versus raising in financial markets, You are the chie...

You are the chief financial office (CFO) of Gaga Enterprises, edgy fashion design firm. Your firm needs $10 million to expand production. How do you think the process of raising th

Scope of finance function, SCOPE OF FINANCE FUNCTION In several busine...

SCOPE OF FINANCE FUNCTION In several businesses, based on the complexity and size of financial decision-making, the scope of finance function may be categorized into incidenta

Define advantage and disadvantage of internal rate of return, What are the ...

What are the advantages and disadvantages of the internal rate of return method? The internal rate of return (IRR) method is a discounted cash flow method and a number expressed

Case study on labour standars, describe the impact of different types of st...

describe the impact of different types of standards on motivation, and specifically , the likely effects on motivation of adopting the labor standards recommended for geeta & compa

How many types of segments in the mutual fund industry, How many types of s...

How many types of segments in the mutual fund industry? There are two segments into the mutual fund industry: long-term funds and short-term funds. In Long-term funds bond fund

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