Shout options allow the holder of the option to "shout out" at one or more points during the option life and adjust particular aspects such as the strike price or time to maturity. In some ways, they can be considered as a form of reset options in that the strike price can be reset to a particular level at a certain date.

These options are often generalised as being American-like options due to its shout feature and this produces difficulties in pricing, and analytical closed form solutions are not available.

Shout options are often seen embedded in interest rate products and segregated insurance funds.

The payoff function for one shout call and put options can be given as:

Where is the "shout" price at the shout time t and S is the price at maturity.

We have distinguished shout options from reset options based on the fact that we consider reset options to have the resets at predetermined dates, and the reset process is automatic, whereas in shout options, the holder has the right to call reset.

Pricing Using the PDE (Crank-Nicolson, Backwards Difference & Euler's Method):

Windcliff, Vetzal & Forsyth (1999) use the PDE in order to solve the pricing of a shout option directly. They employ several lattice methods to solve the PDE, including the use of implicit finite differences, Crank-Nicolson scheme, and finally, a 2nd order backwards difference method.

By discretising with respect to time, and producing the respective algorithms for each method, they consider the use of extensive lattice nodes near the expiry date to capture the discontinuity characteristics of the shout option.

Even when using variance reduction techniques (namely similarity reduction), it can be shown that with increased refinement levels for convergence (i.e. increasing the number of nodes in the S direction with each level), the computation time is rather intensive, and arguably not viable for practical usage with refinement levels of greater than 2 (see Windcliff, Vetzal & Forsyth (1999)).

Other Known Names / Variants

Extendible Options
Reset Options

Additional/Useful List of resources

Papers:

Black, F. & Scholes, M. "The Pricing of Options & Corporate Liabilities", The Journal of Political Economy (May '73)
Cox, J., Ross, S., & Rubinstein M., “Option Pricing: A Simplified Approach." Journal of Financial Economics, 7. (Sept '79).
Kwok, Y.K., "Shout Options", Working Paper, 2003
Merton, R.,"Theory of Rational Option Pricing", Bell Journal of Economics & Management (June '73)
Windcliff, H., Forsyth, P.A., Vetzal, K.R., "Shout Options: A Framework for Pricing Contracts which can be Modified by the Investor", Journal of Computational and Applied Mathematics, 134, pp. 213-241 (2001)