21.A "Down and In" put option becomes like a regular European put option only after it is "knocked in."For this to occur, the stock price must fall below a specified level, known as the "in strike" at least once prior to the expiration date.If that never happens, the option expires worthless, regardless of where the stock price is at expiration.

Assume the price of a nondividend paying stock follows a Binomial process, with u = 1.2, d = .8, and R=

1.05.The initial stock price is 100.

a) What is the value of a 2 period European put with a strike price of 100?

b) What is the value of a 2 period 100 strike "Down and In" put with in-strike = 94?. [Alternatives: Simple 2 period binomial valuation problems involving other such options.

An American put is obviously one.Another, one of my favorites during basketball season is this:

"An 'In-your-face' call option is like a regular call option, except that if the stock goes up in every period, the option holder is declared 'stuffed' and the option expires worthless."]