1) You want to buy a binary option on a stock X (X0=$42) with strike K= $43 (ie you earn $1 if the stock price is above K at maturity T and 0 otherwise).At what price will you value this option in the following situations (we consider rf = 3%) ?
a) There are 5 states of the world for the stock price at times t=1 X1= (40,42.5,45,50,60) and the risk-neutral probability vector is the following p=(0.1,0.6,0.2,0.05,0.05)
b) You know the price of the following calls: C(40) = $8.87 , C(42)=$7.83, C(43.5)=$7.13 and C(45)=$6.47 with the notation C(K) = price of the call of strike K. (You can just find a range for the price in this case, hint: think about how traders can give a quick price range for binary option in real life) Consider 1 year to maturity.