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This study applies the Ho & Lee model to value interest rate derivatives.
The advantages of Ho & Lee model include：1. It is easy to apply and extend to
various time length, and 2. the current term structure of
interest rates is taken as
input so that it is consistent to the current business environment.
The main themes of this study include：1. Using the simple regression
method and the calibration approach to estimate the parameters of Ho & Lee
model. 2. Simulating various situations to test how parameters
affect the price of
interest rate derivatives. 3. Applying Ho & Lee model to value swaptions and
swap cancellation.
The evidence is shown as follows：
1. The parameters estimated by the simple regression method are consistent to
the intuition, but they can not be verified to see whether they match the
market because of lacking of options'''' market prices. Besides, it is
impossible to calibrate parameters with swap rates.
2. The effects of the changes of parameters on pricing
interest rate derivatives
are：
(1) Initial term structure of interest rate：The slope and intercept of initial
yield curve are positively correlated with call value, and negatively
correlated with put value. Besides, the required minimumδthat prevents
negative interest rate is smaller when the slope or intercept is higher.
(2) The value ofδ：Whatever interest rate derivatives are, the smaller δ,
the higher their values.
(3) Exercise rate and expiration date of various interest rate derivatives：
Rising exercise rate follows the lower call value and higher put value. On
the other hand, the relation between expiration date of European interest
rate option and its value doesn''''t necessarily exist, but the value changes
in accordance with the expectation implied in the yield curve.
(4) Time partition：In most examples , the less time partitions, the higher
the prices of interest rate options.
3. On valuing swaptions and swap cancellation, the results are：
(1) Regardless of the initial yield curve, the longer maturity of underlying
interest rate swap has the higher call swaption value. Besides, this
evidence tends to enlarge as the slope or intercept of yield curve is
increased.
(2) The difference between the values of American and European interest
rate swaption seems to be positively correlated with the slope(absolute
value) and intercept of the initial yield curve.
(3) Having an IRS cancellation is like to own an ordinary interest rate option,
but uncertainties of future interest rate make the decision and valuation of
swap cancellation need to do further consideration.
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