Question

Intro A bank agreed to an interest rate swap with a company. Under the terms of the swap, the bank pays 4.4% per annum (compounded semiannually) every six months and receives six-month LIBOR in return, for 10 years on a notional principal of $200 million. Today, when the swap has a remaining life of 2.5 years, the company defaults on the swap and will not make the promised floating payment (the bank will not make a reciprocating payment either). The company will not make any other payments in the future. OIS rates are 3.8% for all maturities (with continuous compounding) and LIBOR rates are 4.9% for all maturities (with semiannual compounding). On the last payment date, the 6-month LIBOR forward rate was 4.1%. Part 1 Attempt 1/4 for 10pts. What is the loss to the bank (in absolute terms, \$ million)?

Answer 1

To estimate the loss to the bank due to the company defaulting on the interest rate swap, the present value of future fixed payments the bank would have made is determined using the OIS rate for discounting. The fixed payments are known, but as the company defaults, the LIBOR-related payments are nullified. Thus, the loss is solely based on the present value of the fixed payments, offset by the adjustment due to the last known LIBOR rate.

Step-by-step explanation:

To calculate the loss to the bank as a result of the company defaulting on the interest rate swap, we need to determine the present value of the future cash flows the bank would have received and compare it to the present value of the cash flows the bank would have paid. This requires comparing the fixed rate payments of 4.4% per annum, compounded semiannually, to the floating six-month LIBOR payments.

The present value of the fixed rate payments that the bank would have made can be found using the formula for the present value of an annuity. Because the interest rate is compounded semiannually, there will be a total of 5 payments (2.5 years × 2 payments per year). The semiannual payment amount on the notional principal of $200 million will be 0.044 × $200 million / 2 = $4.4 million per payment.

The present value of these fixed payments at the OIS rate (with continuous compounding) is calculated using the formula PV = Payment × (1 - e^{-rate × time}) / (rate per period), where 'rate' is the continuous OIS rate, and 'time' is the time in years for each payment.

The present value of the floating LIBOR payments that the bank would have received is more complex because it involves estimating the future LIBOR rates. However, since the company has defaulted, the bank will make no further payments, and the LIBOR rate is irrelevant for future payments. Hence, the bank's loss is simply the present value of the fixed payments it no longer has to make, offset by the last known forward LIBOR rate adjustment.

Without concrete numbers or further details on the LIBOR rate adjustment, we can't provide an exact numerical answer for the loss to the bank. However, the process described outlines the approach one would take to calculate the loss in absolute terms, in millions of dollars.