Finance Report: Binomial Interest Rate Tree, Spot Rates, and More

This report presents an analysis of the binomial interest rate tree model in finance. It begins by outlining the given spot rates, forward rates, and volatility data. The core of the report involves the construction of a binomial interest rate tree, detailing the calculations at each node. The report showcases how the binomial interest rate tree is constructed using the provided data including spot rates, forward rates, and volatility. The report includes the formulas used for the calculations and explains how the binomial interest rate tree is created. The report's analysis includes an explanation of how the binomial interest rate tree can be used for valuation, assuming a 50% probability for the upper and lower paths at each period. The report aims to provide a clear understanding of the binomial interest rate tree's application in financial modeling.

Running Head: Finance
Finance
Binomial Interest Rate Tree
Student Name

Finance
Contents
Binomial Interest Rate Tree...................................................................................................................2
Given spot rates:................................................................................................................................2
Given forward rates:..........................................................................................................................2
Given volatility and time-period data:...............................................................................................2
Formulas:...........................................................................................................................................2
Binomial Interest rate tree:...............................................................................................................3
1

Finance
Binomial Interest Rate Tree
Given spot rates:
Spot Rates Percentage
S0 4.20%
S1 4.60%
S2 4.80%
Given forward rates:
Period Forward rates terminology Forward rate values
0 to 1 0F1 4.2000%
1 to 2 1F2 5.0015%
2 to 3 2F3 5.2012%
Given volatility and time-period data:
Volatility per
year 10% Each period
1
year
Formulas:
One year forward rate is denoted by: F
Each period is denoted by: T
2
Upper rate F*exp(volatility*sqrt(T))
Lower rate F*exp(volatility*sqrt(T))
Upper rate
Lower
rate*exp(2*volatility*sqrt(T))

Finance
Binomial Interest rate tree:
This binomial interest rate can be used for the valuation assuming 50% probability for upper and
lower path at each period.
3
6.3528%
5.0015%*EXP(10%*SQRT(1)) 5.2012%*EXP(2*10%*SQRT(1))
5.5275%
4.2000%
5.2012%
(Given)
4.5255%
5.0015%*EXP(-10%*SQRT(1))
4.2584%
5.2012%*EXP(-2*10%*SQRT(1))