Question 1. You live in a country where interest rates may be positive, zero or negative. A negative interest rate means a borrower is credited (rather than charged) interest on a loan, while an investor is charged (does not gain) interest on a deposit. As usual, denote the continuously compounded interest rate (whether positive, zero, or negative) by r.

(a) In no more than a paragraph, explain in general terms the circumstances that might give rise to a negative interest rate, and the intentions of the central bank in adopting it.

(b) As you know, the holder of a forward contract agrees to deliver or take delivery at time T of an asset (St) for a price F0 agreed on at time 0. Suppose r

(c) Give a rigorous proof, using principles we adopt in the course, of your choice in Part (b). State the principle(s) you use.

(d) Suppose r > 0. Which of the following is correct? Give reasons.

(i) Fo = Soert; or (ii) Fo = Soe-IrT; or (iii) Fo (iii) Fo = Soe-rT (i) Fo = Soert; or (ii) Fo = Soe-lr|7; or (iii) Fo = Soe-rT (i) Fo = Soert; or (ii) Fo = Soe-IrT; or (iii) Fo (iii) Fo = Soe-rT (i) Fo = Soert; or (ii) Fo = Soe-lr|7; or (iii) Fo = Soe-rT