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Suppose that the price of interest rate risk is constant and that the spot rate r t follows the first - order autoregressive process under
Suppose that the price of interest rate risk is constant and that the spot rate follows the firstorder autoregressive process under the riskneutral measure:
where iidN so that the logarithm of a zerocoupon bond price with periods to maturity if an affine function of the short rate:
a Derive a formula for the coefficients and in terms of the parameters of the short rate dynamics.
b Evaluate:
c Assuming that derive the process for a oneperiod forward rate in terms of the riskneutral parameters for a very long maturity, What are the implications of the model for the long forward rate? Hint: Note that :
d Now assume that the short rate follows a random walk:
Derive the process for a oneperiod forward rate for a very long maturity, What are the implications of the model for the long forward rate?
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