1 A Dynamic Programming Approach to Price Installment Options

Installment options are Bermudan-style options where the holder period-ically decides whether to exercise or not and then to keep the option alive or not (by paying the installment). We develop a dynamic programming pro-cedure to price installment options. We study in particular the Geometric Brownian Motion case and derive some theoretical properties of the IO con-tract within this framework. We also characterize the range of installments within which the installment option is not redundant with the European contract. Numerical experiments show the method yields monotonically converging prices, and satisfactory trade-offs between accuracy and com-putational time. Our approach is finally applied to installment warrants, which are actively traded on the Australian Stock Exchange. Numerical in-vestigation shows the various capital dilution effects resulting from different installment warrant designs