A binary option is an option which pays you 1 if a certain event happens, and 0 otherwise. Suppose therearetwotimeperiodst=1,2. Youbuytheoptionint=1,anditpaysyouint=2. Inthesecond period, the market return r m is normally distributed, with expected return E [r m] = 0.06, and and standard deviation m = 0.08. The risk-free rate is rf = 0.02. Consider a binary option, which pays 1 if the market's

return is above 0.06, and 0 otherwise. a) (5 points) Calculate the expected payoff of the binary option (note: the payoff means how much you

expect to make from holding the option, ignoring how much you paid upfront to get it) b) (5 points) Suppose the price of the binary option in period 1 is p. Calculate the covariance of the binary

option's return with the market return r m. The answer should be a function of p. (Hint: suppose r

2 follows a normal distribution with mean and standard deviation , then E [(r ) | r > ] = .)

c) (5 points) For (c)-(d), suppose that CAPM holds and that the covariance between the binary option's return and the market return is m,option. Calculate what the expected return on the binary option must be. The answer should be a function of m,option.

d) (5 points) What must be the price of the binary option in t = 1?