Consider a two-period binomial model in which a stock currently priced
at $10 will be worth, in exactly one year from now, $15 with
probability .6 or $5 with probability .4. There is a risk-free bond
with a one-period interest rate of 5%. A digital call option is a
derivative security that pays $1 upon expiration if the price of the
underlying stock is above the strike price and nothing if it is below
the strike price. Calculate the arbitrage price today of the digital
call option with a strike price of $11.