Exact solutions for a strike reset put option and a shout call option

A strike reset put option is a European put option with the added feature that it gives the holder the right to ‘shout’ during the life of the option and thus reset the strike to the then prevailing spot price. The related shout call option is similar to the European call option but has the added feature that the holder can ‘shout’ during the life of the contract to both lock in a profit and reset the strike. This paper derives exact solutions to both of these exotic options.