Where ....... are first order partial derivatives with respect to t and S and C a second order partial derivatives with respect to t and S. The boundary conditions for a standard call option which expires at .....(.... ‘non-average’ option) can be expressed as:
For an AV-options, however, the boundary condition at time.. implies that the value of the option is equal to ...... . We recall that before this value can be calculated, the (AV-options) has to be valued over the time interval [...], and that .... in that case depends on t,..and ....