Shout options: a framework for pricing contracts which can be modified by the investor

A shout option may be broadly defined as a financial contract which can be modified by the holder according to specified rules. In a simple example, the holder could have the right to set the strike of an option equal to the current value of the underlying asset. In such a case, the holder effectively has the right to select when to take ownership of an at-the-money option. More generally, the holder could have multiple rights along these lines, in some cases with a limit placed on the number of rights which may be exercised within a given time period (e.g., four times per year). The value of these types of contracts can be estimated by solving a system of interdependent linear complementarity problems. This paper describes a general framework for the valuation of complex types of shout options. Numerical issues related to interpolation and choice of timestepping method are considered in detail. Some illustrative examples are provided.