Suppose that the following spot rates are provided by central London banks (LIBOR, the London Interbank Offer Rate, is the rate at which money can be deposited; LIBID, the London Interbank Bid Rate, is the rate at which money can be borrowed):

Question

Rate LIBOR LIBID
1 month 8.41% 8.59%
2 months 8.44% 8.64%
3 months 9.01% 9.23%
6 months 9.35% 9.54%

As a bank manager acting for a customer who wishes to arrange a loan of $100, 000 in a month’s time for a period of 5 months, what rate could you offer and how would you construct the loan? Suppose that another institution
offers the possibility of making a deposit for 4 months, starting 2 months from now, at a rate of 10.23%. Does this present an arbitrage opportunity? All rates stated in this exercise are continuous compounding rates.

Accepted Answer

You need to deposit [latex]100, 000e^{−8.41\%/12} ≅ 99, 301.62[/latex] dollars for one month, which will grow to the desired level of $100, 000, and borrow the same amount for 6 months at 9.54%. Your customer will receive $100, 000 after 1 month and will have to pay 99, [latex]1301.62e^{9.54\%/2 } ≅ 104, 153.09 [/latex] 1 dollars after 6 months, which implies a forward rate of 9.77%. (The rate can be obtained directly from (10.5).) The rate for a 4-month loan starting in 2 months is

[latex]f(0,M,N) =\frac{N_y(0,N) − M_y(0,M)}{N −M} [/latex] (10.5)

[latex]f(0,M,N) =\frac{6 × 9.35\% − 2 × 8.64\%}{4}\cong 10.09\%, [/latex]

so a deposit at 10.23% would give an arbitrage opportunity.

Question 10.18: Suppose that the following spot rates are provided by centra...

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