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. © 2001 Elsevier Science B.V. All rights reserved.
Windcliff, H., Forsyth, P. A., & Vetzal, K. R. (2001). Shout options: A framework for pricing contracts which can be modified by the investor. Journal of Computational and Applied Mathematics, 134(1–2), 213–241. https://doi.org/10.1016/S0377-0427(00)00551-3