Notional principal

At the same time the equity weighting needs to be increased and this can be achieved by dividing the notional principal by the value of the Dow Jones EuroSTOXX futures contract and using the result to adjust the portfolio s beta. 

One solution to this problem, of course, is for the company to enter into a 5-year interest rate swap on a notional principal of 1 million, agreeing to pay the fixed rate and receive the floating rate. In our illustration, the fixed rate might be 3%, in which case the company would effectively lock into paying the fixed rate of 3% per annum over the 5-year period. While this protects the company against higher interest rates, the company cannot benefit from lower rates, especially at the outset when rates are just 2%. 

In this way, an interest rate cap allows the borrowing company to benefit when interest rates are low, while protecting the company when interest rates are high. This is marvellous, as it provides the best of both worlds, but such a result does not come free As with other interest rate options, the company would have to pay an up-front premium to purchase the cap. In the example here, this up-front premium might be around 165 bp of the notional principal, i.e., 16,500, which is equivalent to around 35 bp per annum if this cost were spread over the lifetime of the cap. This caps the effective EURIBOR at around 3.35% rather than 3%. Contrast this with the interest rate swap, which does not involve an up-front payment, but penalizes the company with a higher initial interest rate instead. 

By convention, caps are quoted as an up-front premium expressed as a percentage of the notional principal. So in the above example, the cap would be quoted at 1.65% or 165 bp. 

The buyer of this swaption has the right, one year from now, to enter into a 3-year swap as the fixed-rate payer, paying 4% p.a. against receiving 3-month EURIBOR, on a notional principal of 10 million. If 3-year swap rates on 29 March 20X4 were, say, 4.5%, it would be worthwhile for the owner to exercise the swaption, paying a fixed rate of only 4% when the market rate was 4.5%. 

By effectively embedding caps and/or floors on a notional principal equal to a multiple of the underlying bond s face value, a company can offer investors significantly higher current yields, but with the risk that future returns could fall markedly if rates rose beyond a certain level. 

The structure is achieved by XYZ effectively buying 5-year caps struck at 4.50% on five times the notional principal of the note issued. Eor example, if XYZ issued notes with a face value of 10 million, it would effectively buy interest rate caps from investors with a notional principal of 50 million. The up-front premium of 19 bp in this example, therefore, becomes geared up to 95 bp, equivalent to 20 bp p.a. This enables the investor to receive their enhanced coupon, but the geared payment from the caps sold means that investors return diminishes rapidly in any period where EURIBOR sets above 4.50%. 

With a vanilla cap, the notional principal remains constant throughout the lifetime of the product. However, a customer might need an interest rate cap linked to a loan which is steadily being paid down over time. 

To match the declining principal outstanding on the loan, a bank could create an amortising cap, in which the notional principal reduces in line with that of the loan. 

If the cap s notional principal increases steadily over time, it is called an accreting cap, and if the notional principal increases in some periods and reduces in others, it is called a rollercoaster cap. In all cases, however, the schedule of notional principals must be agreed in advance—this cannot be left to the whim of the customer later on. 

These products are no more difficult for a bank to price than vanilla caps. The bank has to price each caplet individually anyway, so pricing the strip with different notional principals each period does not complicate the calculation unduly. 

Selling a floor at the same strike rate but for a lower notional principal, to match the cap premium exactly. 

If 3-month EURIBOR stays within range, as the investor expects, he or she will keep the premium from the DNT option, which is equivalent to 2.25% of the notional principal. Together with the 4.50% income from the vanilla note, the investor receives the enhanced yield of 6.75%. 

If, on the other hand, 3-month EURIBOR trades outside the range— even on a single day—this will trigger the payout from the DNT option. The investor will then have to pay out 6.75% of the notional principal, which exactly wipes out the income from the vanilla bond plus the option, leaving him with zero income, but the principal intact. 

Swaptions are options that allow the buyer to obtain at a future time one position in a swap contract. It is quite elementary that an interest rate swap, fixed for floating, can be understood as a portfolio of bonds.To consider this assume that the notional principal is 1. Then the claim on the fixed payments is the same as a bond paying coupons with the rate p and no principal. Let X be the time when the swap is conceived. The claim on the fixed income stream is worth, at time X,... 

In an interest rate swap, the counterparties agree to exchange periodic interest payments. The euro amount of the interest payments exchanged is based on the notional principal. In the most common type of swap, there is a fixed-rate payer and a fixed-rate receiver. The convention for quoting swap rates is that a swap dealer sets the floating rate equal to the reference rate and then quotes the fixed rate that will apply. 

An interest rate swap is an agreement between two counterparties to make periodic interest payments to one another during the life of the swap. These payments take place on a predetermined set of dates and are based on a notional principal amount. The principal is notional because it is never physically exchanged—hence the off-balance-sheet status of the transaction—but serves merely as a basis for calculating the interest payments. 

An interest rate swap is thus an agreement between two parties to exchange a stream of cash flows that are calculated hy applying different interest rates to a notional principal. For example, in a trade between Bank A and Bank B, Bank A may agree to pay fixed semiannual coupons of 10 percent on a notional principal of 1 million in return for receiving from Bank B the prevailing 6-month LIBOR rate applied to the same principal. The known cash flow is Bank As fixed payment of 50,000 every six months to Bank B. 

Consider a plain vanilla interest rate swap with a notional principal of M that pays n interest payments through its maturity date, T. Payments are made on dates 4 where i = 1,. ..n. The present value today of a future payment made at time r, is denoted as PV 0, t,). If the swap rate is r, the present value of the fixed-leg payments, PVfi s is given by equation (7.2). 

The first term in (7-18) represents the notional principal multiplied by the discount factor 1. This reflects the fact that the present value of an amount received immediately is the amount itself. 

The notional principal remains constant during the life of the swap... 

A differential swap is a basis swap in which one of the legs is calculated in a diflFerent currency. Typically, this leg is linked to a reference index rate for another currency but is denominated in the domestic currency. For example, one party might pay 6-month sterling LIBOR, in sterling, on a notional principal of 10 million and receive euro-LIBOR minus a margin, in sterling, on the same notional principal. Differential swaps are not very common and are the most difficult for a bank to hedge. 

In an accreting, or step-up, swap, the notional principal increases over the life of the swap in an amortizing the principle decreases. Swaps whose notional principal fluctuates—increasing one year and decreasing the next, for example—are known as roller coasters. 

Equation (7.24) essentially states that PVBP of the swap equals the difference between the PVBPs of the fixed- and floating-rate bonds. This value is usually calculated for a notional principal of 1 million, based on the duration and modified duration of the bonds (defined in chapter 2) and assuming a parallel shift in the yield curve. 

Receive Loan CF = (+Libor-I-330) x l(Loan Notional Principal)... 

The floating-leg payments of an interest rate swap can be valued using just the discount factor for the final maturity period and the notional principal. This short-cut method is based on the fact that the value of the floating-leg interest payments is conceptually the same as that of a strategy... 

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