n*********3
发帖数: 21 | 1 from risk neutral bond pricing we know
P(t,T) = E[exp(-\int_t^T r(s)ds)]
If we think of Vasicek model:
dr(t) = a(b-r(t))*dt + sigma*dWt
We have analytical solution for r(t) (from http://en.wikipedia.org/wiki/Vasicek_model), but how to calculate P(t,T) based on the r(t)?
So far, I got stuck when facing E[-\int_t^T r(s)ds] and Var[-\int_t^T r(s)ds] | c****o
发帖数: 1280 | 2
ds]
you can think of E[-\int_t^T r(s)ds] as a double integral, then use the
fubini theorem to interchange the order of intergral, actually,
E[-\int_t^T r(s)ds] =-\int_t^T(E(r(s))ds,similarly for variance.
【在 n*********3 的大作中提到】
: from risk neutral bond pricing we know
: P(t,T) = E[exp(-\int_t^T r(s)ds)]
: If we think of Vasicek model:
: dr(t) = a(b-r(t))*dt + sigma*dWt
: We have analytical solution for r(t) (from http://en.wikipedia.org/wiki/Vasicek_model), but how to calculate P(t,T) based on the r(t)?
: So far, I got stuck when facing E[-\int_t^T r(s)ds] and Var[-\int_t^T r(s)ds]
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