Installment options are Bermudan-style options where the holder periodically decides whether to exercise or not and then to keep the option alive or not (by paying the installment). We develop a dynamic programming procedure to price installment options. We derive the range of installments within which the installment option is not redundant with the European contract. Simulations analysis shows the method yields monotonically converging prices, and satisfactory trade-offs between accuracy and computational time. In addition, we examine the flexibility in installment option design that yields various hedging properties. Our approach is applied to installment warrants, which are actively traded on the Australian Stock Exchange. Numerical investigation shows the various capital dilution effects resulting from different installment warrant designs.

We study the utility based pricing of arbitrary contingent claims in a semi-martingale model of incomplete financial market. In order to avoid artificial smoothness assumptions, we replace the differential condition studied by Davis [1997] by an optimality criterion which generalizes it. Our main results concern the uniqueness of the utility based price and show that this uniqueness is equivalent to the differentiability of the agent’s indirect utility function. In particular, we establish that a necessary and sufficient condition for all bounded claims to admit a unique fair price is that the normalized marginal utility defines an equivalent martingale measure and construct an explicit counterexample showing that even in the case where the utility function is smooth there are bounded claims for which the corresponding indirect utility function is non smooth.

Proven to be less expensive and more efficient than a set of individual options, basket options are now commonly used by treasury managers to hedge the different risks faced by non-financial institutions. In this article, we make the design of a basket option on commodity prices with stochastic convenience yields, exchange rates and zero-coupon bonds. We carry out Monte Carlo simulations to value this basket option. Then, we use the maximum likelihood method to estimate the different parameters of the theoretical model proposed as well as the correlations between these variables. As done in Duan (1994), we apply the maximum likelihood approach adapted to unobservable variables to estimate the temporal series of the convenience yield as well as its parameters. Finally, Monte Carlo studies are conducted to examine the performance of the maximum likelihood technique in finite samples.