Up-front premium

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. 

Effectively, the investor has sold XYZ a 3-year cap on 6-month EURIBOR struck at 3% for an up-front premium of 33 bp, equivalent to 11 bp p.a. XYZ keeps 1 bp of this annual premium, and uses the other 10 bp to pay the enhanced margin above EURIBOR. 

In this case the investor has effectively bought from XYZ a 3-year floor on 6-month EURIBOR struck at 2% for an up-front premium of around 2 bp (very cheap), equivalent to less than 1 bp p.a. over three years. XYZ deducts 2 bp from its normal EURIBOR margin to offer investors a slightly lower yield of EURIBOR plus 38 bp right now, in return for guaranteeing that the rate cannot fall any lower. XYZ uses 1 bp of the 2 bp deduction to buy the 3-year floor (perhaps from a bank), and keeps the other 1 bp itself. 

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%. 

The solution is a step-up cap, where the strike rate might be set at 50 bp above the forward rate for each interest period. The strike rate might be 2.75% in the first period, rising to 5.50% for the final six-month period. The up-front premium for such a cap might be just 49 bp (equivalent to just 11 bp p.a.), half the cost compared to 87 bp up-front (19 bp p.a.) for a vanilla cap struck at a level 4%. 

These are an attractive product for the borrower who is required (perhaps by mandate) to obtain protection against higher interest rates, but who doesn t think that such protection is really needed. A self-funding cap has no up-front premium payment. Moreover, if interest rates stay below the strike rate, no premium is payable in arrears, either. Only when rates rise through the strike rate is a premium eventually payable, but this is typically double what the vanilla premium would have been. 

Maximum losses are floored at around 700,000, similar to those with the ATM options, but the up-front premium cost is almost zero, comparing very favourably with the cost of the ATM options in excess of 600,000. If the investor is wrong, and bond prices continue to rise, the investor can still enjoy the benefit of a rise in bond prices of more than 1.50% before the calls sold cap the investor s profits at around 800,000. For many investors in this position, the price collar is an excellent strategy. 

To illustrate this, suppose that the company now wants to cap its borrowing costs at 3.5%. From Exhibit 17.27 we can see that the up-front premium for a 5-year cap struck at 3.5% is 84 bp. A floor struck at the same rate would be priced at 2.40%, almost three times as expensive. Given these quotations, suppose the company ... 

Buys a 5-year cap struck at 3.5% on 10 million, priced at 84 bp, therefore paying an up-front premium of 84,000. 

A neat way round this problem is to reduce the fixed rate of the swap below the market s fair rate of 3.00%, and have the swap counterparty make an up-front payment to the investor to restore parity. Reducing the swap rate also means that the strike rate of the payer s swaption must also be reduced in line, which increases the up-front premium payable. 

The opposite is true for an option seller, whose value profile is shown in Exhibit 17.2. The option seller can only lose, not gain. No one in their right mind would therefore sell options for free Instead, the option buyer must pay a premium to the option seller to acquire the rights conferred by the option. This is another important distinction between options and other derivatives (like swaps and forward rate agreements) for which no up-front payment is due. 

Moneyness—Is the option worth exercising If so, it is said to be in-the-money (ITM). Our call option struck at 98 would be in-the-money if the underlying bond was trading above 98. If the bond were trading below 98, the call would instead be out-of-the-money (OTM). Finally, if the current price of the underlying asset was the same as the strike price, 98 in this example, the option would be at-the-money (ATM). Premium—The amount paid by the buyer of an option is called the premium. This is normally paid up-front. 

Unlike the OTC options that we shall be examining later, the premium for these exchange-traded options is not actually paid up-front. Instead, until exercise or expiry, the option buyer and seller are both margined in the same way as with futures positions. The premium of 11,800 is only paid—again through the margining system—when the option expires or is exercised. ... 

As an example, let s suppose the company bought a 5-year cap with a slightly higher strike rate of 3.50% at an up-front cost of 84 bp, and sold a 2.50% floor to bring in 30bp premium up-front. The premium income from the floor reduces the net cost by 35% to just 54 bp upfront, equivalent to 12 bp per annum if spread over five years. 

The company obtains the quotations shown in Exhibit 17.27 for 5-year cap and floor premiums, each one expressed as an up-front percentage... 

The company chooses the 4% strike cap is being the best compromise between up-front cost and level of protection. It then asks its bank to find the floor strike such that the floor premium is also 41 bp, matching the premium for the 5-year cap. From Exhibit 17.27 it is apparent that the floor strike must lie between 2.50% and 2.75%, and the exact figure turns out to be 2.59%. 

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