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INTRODUCTION
This chapter offers a brief overview of the vast range of innovative OTC derivatives and hybrid securities. It provides an idea of the investment alternatives at clients’ disposal. Some are traded in large volumes and are relatively simple to price using standard models, whilst others are extremely complex. Due to their number and nature, only a brief description is given.
OTC DERIVATIVES
Caps, floors and collars
Caps, floors and collars are OTC interest rate derivatives that offer a buyer a right, but not the obligation to secure the lending/borrowing rate. Unlike option contracts that have a single expiry date, they have periodic resets until maturity. Theoretically, the same protection could be achieved by purchasing a strip of options with different maturities that would cover the required period. But in practice the premium and margin requirements, as well as the management of a large number of transactions, would make this solution impractical.
Interest rate caps offer the buyer the right but not the obligation to fix the borrowing interest rate for a period of time, with regular reset periods against a benchmark (typically three-month Libor) in exchange for the premium payable up-front. They are in effect a strip of call options (caplets) as well as an OTC alternative to a strip of put options on interest rate futures. They can be priced using a slight modification of the standard Black–Scholes model. However, care must be taken over whether the caps are seen as puts on futures, or calls on interest rates, as the correct quotations and relevant volatilities must be used.
Interest rate floors offer the buyer the right but not the obligation to fix the lending interest rate for a period of time with regular reset periods against a benchmark (typically three-month Libor) in exchange for the premium payable up-front. Using the above analogy, they can be constructed using a strip of put options, or a strip of call options on interest rate futures. Depending on whether they are seen as calls or puts, either the Black–Scholes formula can be used directly, or their price can be derived from the put–call parity relationship.
Interest rate collars or (cylinders) are combinations of caps and floors, whereby the range of acceptable rates is fixed. They can be seen as either borrower’s collars (buying a call for upward protection and selling a put and limiting benefits of downward interest rate movements), or as lender’s collars (selling a call and buying a put). As the buyer is forgoing the benefits of a rate decrease below the floor level, the collars are much cheaper than caps and floors. The put and call strikes can be set in such a way as to provide a zero-cost collar.
Interest rate guarantees are one-period caps and floors, i.e. options on FRAs.
Captions and floorptions are options on caps and floors, and hence offer an investor an opportunity to abandon the cap or floor agreement if not needed. They are useful to investors who are uncertain if they will need floating rate financing in the future.
Swaptions are options on swaps (typically coupon swaps). The motivation for trades is the same as for caps, but unlike caps that have multiple exercise dates, the swaptions have only one and therefore have to exchange future payments even if that is no longer beneficial to the buyer. This makes them a cheaper alternative to caps.
Rate spread options offer an exposure to the basis between two benchmark rates (e.g. three-month Libor vs. six-month Libor).
Better performance bond options allow the buyer to receive the greater of two assets’ returns over a specified period of time as long as they are both positive.
Structured finance products
Swap-linked notes exploit the difference in characteristics of long- and short-term bonds. Even though all bond prices rise with falls in yield, the impact is higher for bonds with greater duration (longer maturity and lower coupon). Long dated bonds also have less volatile yields compared to the short-term issues. Investors who do not wish to compromise between the two enter into swap-linked notes whereby the redemption value of a short-term note is linked to a long-term swap rate.
Delayed reset floaters or Libor in arrears swaps fix the floating leg of the swap only a few days before the payment is due, which is in contrast to standard swap arrangements where the rate is fixed at the beginning of the reset period and paid at the end. Clearly in a rising interest rate environment this is advantageous to the investor and this type of swap is more expensive than its ‘vanilla’ counterpart and vice versa.
Reverse floating rate notes (reverse FRNs) are short-term swap structures that offer an alternative to the classic FRNs which pay a fixed coupon in exchange for a floating rate in order to fix the cost of borrowing when rates are expected to rise. Reverse FRNs offer a potential gain is such a case, as their floating rates fall as the Libor increases (e.g. they pay 10 per cent – Libor). Hence under FRN, to protect against interest rate falls, the investor should receive the fixed rate, whilst to exploit increases in Libor, the floating rate should be received.
Capped/collared floaters are FRNs that set the limits on the floating coupon rate, either by limiting the potential profit (using caps only), or by fixing both the maximum and minimum level (using collars). In comparison to FRNs, capped FRNs are a cheaper alternative as their price incorporates a series of short call option premiums. Collars comprise both short calls and long puts, therefore depending on the strikes of the options bought and sold, collared FRNs can either be more expensive than capped versions, or they can incorporate OTM calls that offset a cheap purchase of a floor above prevailing market rates (thus making them a very cost-effective strategy).
Exotic options
Variation on standard option specification
Bermudan options are options with exercise specifications halfway between European (exercised at expiry only) and American options (exercised at any point until expiry). They offer several specific exercise dates during the option contract, which is an attractive prospect for an investor who may wish to have an option to cancel a swap at each coupon reset date.
Digital/Binary options pay a fixed amount on exercise, regardless of how much the option is in the money as long as it is ITM at expiry (all-or-nothing options) or if it has been ITM at any point until expiry (one-touch options). The payout from a short binary option can be approximated for hedging purposes by using a bull call spread strategy with narrowly spaced strikes (shown in Appendix 1).
Contingent options do not require up-front premium payment. It is only due if the option is exercised, but if the option is ITM, even by an amount smaller than the premium, it must be exercised. Their payoff profile is equivalent to a combination of long call/put and short digital call/put.
Chooser options are options that give the buyer the choice whether to exercise call or a put at a later date. These are single options that effectively incorporate call on a call and call on a put, each with zero strike. Their valuation is halfway between an ordinary call and a straddle (see Appendix 1).
Delayed options are options that give the buyer the right to receive at a future date another option with the strike set at the prevailing market value of the underlying on that date.
Path-dependent options
Average rate – Asian options do not pay the difference between the underlying and the option strike at exercise; the difference between the average price of the underlying and the strike is paid instead. The averaging can be done arithmetically or geometrically and can be applied to a period equal to the lifetime of the option, or just a part of it.
Average strike options, in contrast to Asian options, have the strike set to the average price of the underlying; the difference between the strike and the prevailing market price of underlying is paid on exercise.
Look-back options allow the buyer to set the strike at expiry to the most favourable value the underlying has achieved over the lifetime of the option. Obviously they are much more expensive than the standard options, as they have a much higher probability of expiring ITM, hence they are also known as ‘no regret options’.
Barrier (knock-in or knock-out) or trigger options are activated or extinguished when the value of the underlying reaches a predetermined level. Regular barrier options start off as being activated (the barrier is set at a deeper OTM level than the strike) and are extinguished if the barrier is touched or crossed over. Reverse barriers start off as inactive (the barrier is set at a deeper ITM level than the strike) and are triggered once the barrier is touched or crossed over. Therefore this gives rise to four possible scenarios:
- Down and out calls (option extinguished at barrier, as it is OTM anyway)
- Up and in calls (option activated only when it is deeper ITM than the strike)
- Up and out puts (option extinguished at barrier)
- Down and in puts (option activated at barrier).
As the above options can be extinguished or may never even be activated, their premiums are much lower than for standard options. They are favoured by investors with a definite view of the market direction, providing them with a cheap investment strategy.
Cliquet or ratchet options are options with the strike reset at the prevailing underlying price at predetermined dates until option expiry, locking in their intrinsic value.
Ladder options are similar to cliquet options, but the strike is reset if and when the underlying price reaches predetermined levels during the lifetime of the option. They are harder to price, as there is an additional level of uncertainty. In the above scenario, the fixing dates were known but the underlying prices were not, whilst the ladder options are affected both by the uncertainty in the underlying value as well as the timing of resets.
Shout options give the investor the right to ‘shout’ when they wish to reset the strike value, regardless of the underlying value. The number of ‘shouts’ is typically limited.
Multi-factor options
Rainbow or outperformance options, if exercised, pay the buyer the difference between the best price and the strike (for call options) or the worst price and the strike (for put options) from a number of underlying securities. Obviously they are more expensive than standard option contracts.
Basket options pay to the investor the difference between the option strike and the average price of the basket of underlying assets. Pricing these derivatives is highly affected by the correlation of the underlying assets, type and the variance of their price distribution.
Spread options, if exercised, pay the difference between two asset prices. The strike can be set in relation to one of the assets, but if the option expires ITM the payout is based on the difference between the two assets.
Quanto options have their payout linked to one underlying value, but the amount is determined in reference to another asset. For example, the strike is set relative to the three-month Libor, but once the option is exercised the payoff is EUR denominated.
HYBRID SECURITIES
The term ‘hybrid securities’ refers to financial instruments that have properties of two or more unrelated securities, typically traded in their own specialised markets. In financial markets this term is adopted for the class of products that link debt and equity markets.
Even though hybrids have existed in various forms for a while, their popularity has grown in recent years since accounting regulations allowed them to be recorded largely as ‘off-balance sheet’ instruments. This enabled companies to trade in much larger volumes; typically issuing hybrids (to gain access to low-cost funds) and with their proceeds repurchasing equity shares for much higher returns. Below are some examples of various types of hybrid securities.
Convertible bonds
Convertible bonds are bonds with the call option attached that gives the holder the right but not the obligation to convert the bond into equity shares in the company that issued the bond. The option can be exercised at only one specified date (European style), or a series of predetermined dates (Bermudan). This optionality comes at a price, as the bond typically pays a lower coupon than a comparable issue without the conversion optionality attached. Valuation of convertibles is very complex, due to many underlying factors affecting their price. Typical approaches are: option pricing model (a variation of Black–Scholes), dividend valuation model or cross-over method. The Black–Scholes model is covered in Chapter 9, whilst the remaining two are outside the scope of this book.
Callable bonds
A callable bond gives the issuer the right but not the obligation to buy back at a future date the bond from the investors at the price agreed at inception. Clearly the coupon on this type of bond is higher than for a comparable bond without the optionality, as the investors receive the option premium as a compensation for the risk undertaken. From the investors’ point of view the callable bond is the combination of straight bond and short call option, hence:
Value of callable bond = Value of straight bond – Call option
As the option value increases, the price of the callable bond decreases (bond yield increases). The amount of this change is determined by the interest rate environment.
In a low interest rate market, the price of the straight bond will increase, but the call option to buy it back at lower strike will also be high, leaving the value virtually unchanged.
In a high interest rate environment, the price of the straight bond will be low, but the option will be deeply OTM, hence worthless. Any further small changes in interest rates will have no effect on its value. Therefore, the callable bond follows the behaviour of the straight bond.
In a highly volatile interest rate environment, the value of a call option will significantly increase (as the probability of exercise increases), reducing the value of the callable bond.
Puttable bonds
A puttable bond gives the investor the right but not the obligation to sell the bond back to the issuer at a future date at the price agreed at inception. Using the earlier logic, the coupon on this type of bond is lower than for a comparable bond without the optionality, as the investors pay the put option premium to compensate the issuer for the risk undertaken. From the investors’ point of view the puttable bond is the combination of straight bond and long put option, hence:
Value of puttable bond = Value of straight bond + Put option
In contrast to the callable bonds, as the option value increases, the price of the puttable bond also increases. The amount of this change is determined by the interest rate environment.
In a low interest rate market, the price of the straight bond will increase, but the put option will be worthless, leaving the value of puttable bonds comparable to the straight bond.
In a high interest rate environment, the price of the straight bond will be low, but the put option will be ITM, hence valuable. Thus, the value of the puttable bond will be virtually unchanged.
In a highly volatile interest rate environment, the value of the put option will significantly increase (as the probability of exercise increases), increasing the value of the puttable bond.
Both callable and puttable bonds can be priced numerically using the arbitrage-free binomial tree (discussed in Chapter 9).
Dual currency bonds
Dual currency bonds pay interest in one currency but are redeemed in another. This gives the investor the exposure to bond market as well as foreign exchange markets. Further complications arise with the option to fix the exchange rate at the issue date, the redemption date or an average of the two. The investor expects a higher coupon as a compensation for the risk of unfavourable exchange rate moves. From the issuers’ point of view, this is an attractive security. As they operate in the redemption currency, they are not exposed to long-term exchange rate risk.
Mortgage derivatives
Mortgage derivatives are credit derivatives, but the following examples are covered here rather than in Chapter 11, as they are more exotic alternatives to those contracts covered in the previous chapter.
The property market as we know it today would not be possible without mortgages. As the mortgage market developed, so did the investors’ interest in the property sector, resulting in numerous related derivative instruments. Mortgage derivatives refer to contracts whereby the investor receives cashflows based on an underlying pool of mortgages. Some more common variants are discussed below.
Collateralised mortgage obligations (CMOs)
The purpose of CMOs is the distribution of risks and returns from a pool of mortgages tailored to meet clients’ needs. There are many variants of this basic concept, such as:
Sequential pay tranches are instruments where the CMO is split into several tranches ranked as A, B, C etc. The interest from the mortgage obligations is paid to each tranche proportionally to their investment, with tranche A receiving all the income until it is fully repaid. It is followed by tranche B and so on. These are risky investments as the pre-payment schedule, both in timing and the value of the cashflows, is unpredictable. However, property investors who would like a diversified portfolio, but find it impractical or impossible to achieve directly in the physical market, find the CMOs attractive. The upfront cash investment that might purchase only a few specific properties whose mortgage payments could be very volatile creates through the CMO a proportional exposure in a large number of unrelated properties whose overall returns are likely to be more stable. Hence CMOs are popular OTC products.
Stripped mortgage-backed securities are financial instruments based on a pool of mortgages, where the prepayment schedules are not known in advance. The main types are:
- Principal only (PO) securities receive payments based on principal loan amount only, i.e. there are no interest payments. Similar to zero-coupon bonds, they are priced at a discount. The faster the prepayment schedule, the higher the return of a PO.
- Interest only (IO) securities receive only the interest payments based on the loan amount, i.e. there is no principal payment. As the principal is repaid through the PO issue, the value of interest payments under IO decreases. Once the PO is repaid, no further cashflows are due to IO holder. It is a very unpredictable security, as it depends on pre-payment schedules as well as interest rates.
Asset-backed securities
Asset-backed securities are in principle the same as mortgage-backed securities, but the underlying is a pool of assets, such as credit card debt or car loans. Different financial instruments are structured to incorporate asset-backed payments.