Just as we were able to design a cap with a specific cost in mind, we can set the cost of a swaption an analogous way. In this instance, we ask what the fixed rate would have to be, in order to be able to buy the swaption for a price equal to 0.2027 percent of the notional. Again, relying on the market conditions on the trade date (February 7, 2014), forcing the swaption price to this premium would permit us to buy the right to exercise into a forward starting swap with a fixed rate of approximately 0.3010 percent. At the end of the 2014 (i.e., when the first reset date is current), this contract would either have value or not: If the spot, one-year swap fixed rate at that time ends up higher than 0.301 percent, this swaption would be in- the-money, otherwise it would expire worthless. An in-the-money swaption as of January 2, 2015 could either be sold or exercised. If exercised, the resulting swap position would then lock in the cost of funds over the coming 12 months at a rate of 0.301 percent (plus the credit spread) for the coming 12 month horizon.
In comparing these three alternatives, it is important to realize that the pay-up cost of the swap is reflected in the swap’s fixed interest rate, while the initial premiums for the cap and swaption are not reflected in their respective strike prices. For comparability, we need to add the effect of the starting premiums to the respective critical rates (0.4894 percent for the cap and 0.301 percent for the swaption) to get the anticipated worst case outcomes, inclusive of their initial costs.
One way to incorporate these initial costs into our analysis is to appreciate that the present value of an up-front payments (0.2027 percent of the notional for both the cap and the swaption) translates to a step-up in costs from the current LIBOR of 0.24295 percent to the swap’s fixed rate of 0.4420 percent— an increase of 0.1991 percent. (The disparity between 0.1991 percent and 0.2027 percent is a consequence of present value versus future value considerations.)
By adding this same 0.1991 percent to the cap’s strike rate or the fixed rate of the swaption’s underlying forward starting swap, we can generate the effective worst case outcomes of the cap and the swaption, inclusive of their original costs. These adjusted critical rates would then be directly comparable to the 0.4420 percent fixed rate on the swap. For the cap, this all- in worst cast effective cost becomes 0.4894 percent + 0.1991 percent = 0.6885 percent in any given month; for the swaption, the all-in worst case effective cost becomes 0.3010 percent + 0.1991 percent = 0.5001 percent, where the swaption’s worst-case fixed rate would apply uniformly over the 12 months being hedged.
At this point, a hedger should be in a position to compare the three alternatives. A rational choice necessarily incorporates some business judgment about the likely course of interest rate movements throughout the hedge horizon. The greater the certainty of rates rising, the greater the likelihood that the swap will be the preferred hedging vehicle. On the other hand, as that certainty is compromised, the appeal of the cap or the swaption will increase, relative to the swap. Perceptions of volatility will influence the choice between the cap and the swaption, as well. An expectation of greater volatility throughout the accrual periods being hedged would favor the cap relative to the swaption, and vice versa.
No single hedge strategy is best for all market scenarios. If the unhedged cost of funds rises above 0.4420 percent during the hedge horizon, the swap would likely turn out to be the best choice. If rates those costs fall between 0.3010 percent and 0.4420 percent, the swaption would likely be the best. If costs fall below 0.3010 percent, the cap would outperform. While hedges should be designed to protect against the risk of an adverse interest rate move, a prudent choice of the hedging instrument should reflect recognition of the fact that the adverse rate change may not occur.
This article was initially published in the July/August issue of the Association for Financial Professionals' AFP Exhange Magazine