Suppose the short rate r_t is governed by the Vasicek model

where Z_t is a Brownian process under the risk neutral measure Q. Show that the stochastic differential equation of the swap rate K_t[T₀,T_n] under the swap measure Q_S0,n with the annuity numeraire B̂(t ; T₀,T_n) is given by (Schrager and Pelsser, 2006)

where 

Transcribed Image Text:

drt = a(yrt) dt + pdZt,