We present two simple models for the fair value of a self-funding instalment warrant. In the rst model, we assume that the underlying share pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain straightforward numerical solutions with both Monte Carlo and nite-difference methods. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justied when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, in fact, independent of the particular payoff in the first model. We also obtain approximate solutions for the first model which are valid in the small volatility limit by using singular perturbation techniques.
