Risk Management and Financial Institutions, + Web Site, 3rd Edition

APPENDIX D

Valuing Swaps

Aplain vanilla interest rate swap can be valued by assuming that the interest rates that are realized in the future equal today’s forward interest rates. As an example, consider an interest rate swap that has 14 months remaining and a notional principal of $100 million. A fixed rate of 5% per annum is received and LIBOR is paid, with exchanges taking place every six months. Assume that (a) four months ago, the six-month LIBOR rate was 4%, (b) the forward LIBOR interest rate for a six-month period starting in two months is 4.6%, and (c) the forward LIBOR for a six-month period starting in eight months is 5.2%. All rates are expressed with semiannual compounding. Assuming that forward rates are realized, the cash flows on the swap are as shown in Table D.1. (For example, in eight months the fixed-rate cash flow received is 0.5× 0.05× 100, or $2.5 million; the floating-rate cash flow paid is 0.5× 0.046× 100, or 2.3 million.) The value of the swap is the present value of the net cash flows in the final column.1

An alternative approach (which gives the same valuation) is to assume that the swap principal of $100 million is paid and received at the end of the life of the swap. This makes no difference to the value of the swap but allows it to be regarded as the exchange of interest and principal on a fixed-rate bond for interest and principal on a floating-rate bond. The fixed-rate bond’s cash flows can be valued in the usual way. A general rule is that the ...