Question: In 2019 Shell PLC issued bonds for which the holder received no interest but at maturity received the face value of the bond, 1000, (this

In 2019 Shell PLC issued bonds for which the holder received no interest but at maturity received the face value of the bond, 1000, (this is the amount lent by the bondholder to Shell PLC) plus an additional amount, A, which depended on the price of oil at the bond's maturity. This additional amount was set to be 170 times the excess, if any, of the price of a barrel of oil over 25 subject to the condition that the additional amount, A, could not exceed 2550.

(a) Find a formula for A in terms of S (t), the price of a barrel of oil (in dollars per barrel) at the bond's maturity date T.

(b) Express the additional amount in terms of a long position in a number of call options with strike E1 and a short position in a number of call options with strike E2. (Specify both the number and strikes of these call options, which are on the price of a barrel of oil.). Identify what trading strategy the additional amount is equivalent to.

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