Find optimal rational bounds on the one-year contracts

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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

Reference no: EM131168926

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