For each of the following pairs of prices of risky 1-year zero-coupon bond, S, with principal 1, and 1-year riskless zero-coupon bond, Z, with principal 1,
S=0.8,Z=1,
S=0.9,Z=1,
S=0.6,Z=0.9,
S=0.7,Z=1,
Find optimal rational bounds on the following 1-year contracts
(i) a digital call on S struck at 0.9
(ii) a digital put struck at 0.9
(iii) a portfolio of 0.5 digital calls struck at 0.5 and 1 call option struck at 0.75
(iv) a portfolio of 0.5 digital calls struck at 0.6 and 1 digital call option struck at 0.8