This article introduces shout options and offers a pricing spreadsheet. A shout option let investors lock in profits before maturity, but leaves room for future gains.
A shout option offers two (or sometimes more) exercise dates. The first is the maturity time, and the second (the shout date) is set by the holder during the life of the option. The holder “shouts” to fix the asset price at some point before maturity. At maturity, the holder is either paid the payoff at maturity, or the payoff at the shout date.
The payoff of a shout call is C = max(ST – K, L – K, 0), where K is the strike price, ST is the stock price at maturity, and L is the stock price at the shout time. Only shouting when ST > K makes sense.
Shout options are similar to American options and fixed strike lookback options. The asset price of a lookback option, for example, is automatically set to the value which gives the greatest payoff. This puts greater risk on the option writer.
However, shout options require the holder take the risk of guessing the right time to fix the asset price. This means that shout options are cheaper than lookback options.
Pricing Shout Options in Excel
Researchers have proposed several numerical methods to price shout options. This Excel spreadsheet prices a shout option (with one shout date) using a binomial tree in VBA (a Python routine can be found here). It also calculates the Greeks (Delta, Gamma and Theta).
- First, the forward tree is constructed. This uses the standard Cox-Ross-Rubinstein method
- Then the option is valued by travelling back through the tree. At each node, you travel to the end of the tree to calculate the price, assuming that you shouted at that node
At each node, the option value is the larger of (i) the option value if we shout or (ii) the option value if if we do not shout.