Consider the ‘spot dividend’ model, for which the partial differential equation on a call price C(St, t, T ), for a single dividend going ex at time τ is given by:

Show, to first order in the dividend , that an approximate solution for t

and

This approximation is sometimes referred to as the ‘split dividend model’, and can be used as a short cut for approximating calibration of the spot dividend model to European options.

Transcribed Image Text:

t 1 - +(rS Ad(t T)). - + 25202C S2 - - TrC = 0