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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?
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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