Forward measure
In finance, a T-forward measure is a pricing measure equivalent to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity T. The use of forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds. == Mathematical definition == Let B ( T ) = exp ( ∫ 0 T r ( u ) d u ) {\displaystyle B(T)=\exp \left(\int _{0}^{T}r(u)\,du\right)} be the bank account or money market account numeraire and D ( T ) = 1 / B ( T ) = exp ( − ∫ 0 T r ( u ) d u ) {\displaystyle D(T)=1/B(T)=\exp \left(-\int _{0}^{T}r(u)\,du\right)} be the discount factor in the market at time 0 for maturity T. If Q ∗ {\displaystyle Q_{*}} is the risk neutral measure, then the forward measure Q T {\displaystyle Q_{T}} is defined via the Radon–Nikodym derivative given by d Q T d Q ∗ = 1 B ( T ) E Q ∗ [ 1 / B ( T ) ] = D ( T ) E Q ∗ [ D ( T ) ] .