Let Z be a European option whose terminal payoff at date T (>0) is equal to: (B - A) + Max(0: Min(B - S(T); B - A) where S(T) is the value at T of the underlying asset, and A and B (> A) are positive constants. a) Write this payoff as that of a portfolio of a zero-coupon bond and two European calls (with maturity T) whose strikes have to be determined. b) Deduce the theoretical value of option Z at date 0 (the Black-Scholes formula is assumed to be known; you may use a * to denote a discounted value, e.g. Xe T = X*). c) Deduce the sign of its delta (at date 0). Let Z be a European option whose terminal payoff at date T (>0) is equal to: (B - A) + Max(0: Min(B - S(T); B - A) where S(T) is the value at T of the underlying asset, and A and B (> A) are positive constants. a) Write this payoff as that of a portfolio of a zero-coupon bond and two European calls (with maturity T) whose strikes have to be determined. b) Deduce the theoretical value of option Z at date 0 (the Black-Scholes formula is assumed to be known; you may use a * to denote a discounted value, e.g. Xe T = X*). c) Deduce the sign of its delta (at date 0)