WHEN WE BUY A CAR or a new appliance, we need to understand how to use it. We buy it based on what it can do and how it looks. We should know what the parts and processes are—the transmission, engineering, engine, motor, and technology that goes behind its design, assembly, and finally manufacturing—but it is not essential for us to know in detail how each part works. And so it is with financial products. We may not need to know the details of the engineering behind them, but we do need to know what the various instruments are and how we can use them.
Here we explain some of the broad mechanics behind these products. We also provide practical ways to understand the construction and pricing of some of these products.
The products are divided into four families: forwards, options, swaps, and credit. This is depicted in Figure 20.1.
Technically, credit products are a part of the broader fixed income class and use a combination of forwards, options, and swaps in some form. Since their evolution and treatment are different, they deserve, in my view, a separate family for the sake of classification.
The forwards family is essentially a set of price-fixing contracts across asset classes, where two parties agree to buy and sell a particular asset or commodity at a particular price on a particular date in the future. Different date notations are provided in Table 20.1.
Date | Description |
Deal date | Date of transaction, typically the same day |
Value date | Date of actual cash flow, from and to where interest and other calculations are done |
Settlement date | Date at which the transaction or cash flow is settled, typically 2 working days from the value date |
Maturity date | Date of final cash flow after which transaction matures/expires |
Cash date | Settlement is the same as deal date |
Tom date | Settlement is 1 working day after deal date |
Spot date | Settlement is 2 working days after deal date |
Exercise date | Date where the holder of the option decides to exercise or let the option expire |
A simple foreign exchange (FX) forward has already been described in the previous chapter. Here we discuss different kinds of contracts in the forward family and how they can be priced.
Forward prices at any one point of time can either be lower, similar to, or higher than the current spot price. If forward prices are lower than the current spot levels, the condition is referred to as backwardation. If forward prices are higher, the condition is referred to as contango.
The reason why forward prices are different from spot prices is that there is a cost or benefit of holding or carrying the asset for the seller of the asset; this cost could be in the form of interest and dividend (in case of equities). The current valuation of that cost is the difference between the forward price and the spot price.
We cover the conceptual example of a forward price computation for the FX asset class and follow it up with the formula.
Source: Thomson Reuters Eikon
Source: Thomson Reuters Eikon
Sometimes, during casual talk about futures and forwards, the two terms are used interchangeably. Table 20.2 differentiates between the two.
Feature | OTC Forward Contracts | Exchange Futures Contracts |
Transacting parties | Over the counter, between two parties | Party with an exchange |
Nature of contract | Customised | Generalised |
Notional amounts | Customised | Standardised |
Maturity dates | Customised | Generally end of month |
Credit aspect | Using credit facilities (nonfunded) when done with a bank, Using cash or other collateral placed by counterparties with each other | Collateral with exchange |
Usage | Usually more common, when banks can customise exact amounts and delivery dates | Used for generic hedges and also where credit facilities may not be available or amounts may be too small to capture with a bank |
Pricing | Easily available in market information systems for liquid markets Opaque for nonliquid markets | Transparent—available with the exchange at any point of time |
Spread to seller of contract | Banks build in the spread for the firm and can vary from entity to entity depending on relationship and credit standing | Transparent and standardised |
The relationship between the forward price and the expected future spot price has been explained by many economists. From the Treasurer’s viewpoint, however, two things can be inferred:
Figure 20.3 depicts a sample historical performance. It also shows whether the forward hedging strategy would yield a better rate or lesser opportunity loss than the spot price when seeking lower variability.
Data Source: Thomson Reuters Eikon
The different variants of the typical forward contract are representative of the differentiators in customisation of the over-the-counter (OTC) family of products.
A par forward is a single rate for an exchange over a series of forward dates and possibly different notional amounts, with the same forward delivery price. How can a single rate be achieved if the interest rate differentials are different across tenors? The par forward rate is effectively an average rate of all forward dates in the contract, weighted by the notional amount for each date.
Some banks offer variable date forwards. In these, the forward price is fixed while the date for settlement is left at the discretion of the customer (within a range). Here, the price of the forward could be worse than a regular forward, taking into account the bank’s charge for the optionality provided to the customer.
Nondeliverable forwards (NDFs) are forward contracts where cash flows in each currency are not exchanged at maturity. Instead, the amounts are converted back to one currency and net settled. Figure 20.4 gives the example of an NDF.
NDFs are popular with emerging market currencies that have currency convertibility restrictions or exchange control. Hence, NDF markets operate in large financial centres, such as Singapore, London, and New York, for trading forwards across many emerging markets currencies. NDF transactions of a country’s currency are usually not legal in that country (with exceptions) and are also an item of regulatory sensitivity in many countries, owing to central bank views on overseas trading on a currency under its control.
Forward rate agreements (FRAs) are forward interest rates, for different benchmarks such as the London Interbank Offered Rate (LIBOR). While the rates may be easily determined through some quick back-of-the-envelope computations, the rates are readily available from market information systems (see Figure 20.5).
Source: Thomson Reuters Eikon
The notation for a FRA is Start Period × End Period, usually in months. Hence, a 3 × 9 implies a 6-month rate, set 3 months from today (start period = 3 months and end period = 9 months). Figure 20.6 shows the forward curve for the EUR and USD. As can be seen, the shape of the forward curve is generally upward sloping, implying current market views of an increase in short-term interest rates into the future.
Source: Thomson Reuters Eikon
Rate lock is a general term indicating the holding of a particular rate linked to debt. Rate locks can be for a loan (a rate lock fixed by the banker for the client to borrow a committed amount on a committed date for a committed period) or on instruments, such as U.S. Treasury bonds. These rate locks are customised to specific dates that indicate the proposed risk to be managed.
A rate lock with a Treasury bond benchmark, however, is generally linked to a basis risk—the borrowing for the corporate may be linked to the Treasury rate with a spread, but the spread itself may be uncertain.
Forwards and related transactions are some of the most commonly used products owing to the certainty that they provide on cash flows or items being hedged. The sample payoff profile described earlier in Figure 19.19 is depicted again in Figure 20.7. Should the rate move adversely, the buyer of the forward contract would get a better than expected price than an unhedged scenario.
The chief disadvantage of a forward contract is the opportunity loss that it provides by locking in the rate. If the rate moves in favor of the hedger (as shown in the example), having fixed the rate forward, the firm is unable to make use of these moves in its favor.
When using a proxy to hedge forward, such as Treasury bond prices for borrowing or liquid commodity benchmarks (say using WTI Brent to hedge Dubai crude oil), the basis risk of the price differential between the proxy and the actual underlying could still add to variability.
The advent of options and the ability to price options have been key developments that have made financial engineering the wizardry that it is today.
An option is essentially a financial agreement giving the buyer the right, but not the obligation, to buy or sell specified amounts or quantities of an asset or instrument at a specified rate on a specified date.
The vanilla option contract is very similar to insurance. Just as we buy insurance for our car and pay a premium to be compensated in case there is any damage to the vehicle, so too do buyers of options get “insurance” against any specific financial event happening. If there is no car accident (which we hope), the insurance contract expires and is worthless at the end of the period. So too does an option contract for which a premium has been paid: If the financial event (e.g., the stock price moving over 100 or the FX rate moving under 1.20) does not happen, the buyer of the insurance is free to go and procure the same asset or instrument at the prevalent market price since the hazardous event has not happened. In case the financial event has occurred, the buyer of the option has the right to approach the seller (e.g., a bank) and claim back the compensation—in this case, it could be the delivery of the asset or instrument at a predefined better-than-current market rate.
The following note articulates the difference between the right of the buyer of an option and the obligation of the counterparty of a forward.
Various option terminology are presented in Table 20.3. In essence, options are described using these characteristics:
Term | Description |
Call option | Right to buy a commodity or asset. |
Put option | Right to sell a commodity or asset. |
FX-specific terminology | FX options: The call in one currency becomes the put in the other (when we buy one currency, we sell the other currency in the pair). Hence, the notation for FX options cites both currencies: USD call EUR put, or AUD call JPY put. |
Premium | The cost (usually paid up front) for purchasing the option, expressed as a percentage of the notional amount or as a value. |
Strike price | Rate above or below which the option right can be exercised. |
Expiry date | Date on which the right to exercise is determined. |
European-style option | The right to buy (for a call) or sell (for a put) occurs on expiry; most options are European style for settlement. |
American-style option | The right to exercise is available any time up to and before expiry. |
A simple call option payoff is shown in Figure 20.8. The difference between the unhedged position and the hedged position is the option premium; hence, for a spot at expiry below the strike price, the call option payoff is always worse than the unhedged position. Table 20.4 shows the payoff table that explains the respective rate under each scenario.
In this example, the buyer of the option chooses to exercise the option only above 1.70; otherwise, he can get the market rate, which is more beneficial. The worst-case rate is hence quantified, and the buyer knows that the GBP does not have to be purchased at a rate more than 1.73 (including the premium paid up front).
Figure 20.9 shows the put option payoff for a GBP put USD call. Table 20.5 is the corresponding payoff table.
Similarly, the buyer of the right to sell GBP against the USD (i.e., the buyer of the GBP put USD call) knows that, in any scenario, she will not receive less than 1.48 GBP per USD.
How are options priced? Their pricing is based on the famous Black-Scholes formula, which used a then relatively unknown component: volatility. Here we discuss the basic concepts without getting too deeply involved in the mathematics of option pricing. Many great books exist that discuss, model, and debate option pricing, and readers are advised to review them.
There are two things to note about option prices: They are based on forward prices for the tenor, and there are two essential elements of an option price: how far the strike price is from the current forward rate for the same expiry (intrinsic value), and how likely the price is to move in the time left for maturity (time value).
Inputs into option pricing are diagrammatically represented in Figure 20.10.
The intrinsic value is easily discernible from prevalent forward prices and the current spot. Table 20.6 shows how we can determine whether an option is in the money or out of the money for intrinsic value.
At the money (ATM) is the status when the strike is at the current forward level.
The time value, however, depends on the volatility. For a more volatile asset, there is an increased probability that the price will change. Hence the premium is higher for a higher-volatility option.
The volatility used here is implied volatility, usually a market-traded number that the market estimates will be the volatility in the period.
With the advent of the Option Pricer (see Figure 20.11), it has become relatively easy to obtain indicative levels of OTC option pricing. While the final trade will be executed with a bank, for many corporate needs, indicative pricing allows the Treasurer to be aware of where market levels are and to understand different pricing levels across different market conditions.
Source: Thomson Reuters Eikon
The Black-Scholes model remains a very popular pricing basis for many options. The Garman Kohlagen model has been derived to price currency options, incorporating the use of two interest rates (since each currency has an interest rate).
Caps and floors are the interest rate equivalent—a cap on an interest rate benchmark (e.g., LIBOR) is used to put a ceiling on the movement of the interest rate benchmark. A buyer of a cap thus takes the view that interest rates could rise beyond a point and seeks to be compensated through the option should that happen. Caps typically are bought by borrowers to protect against any rises in interest rates beyond the strike price. A sample pricing screen of a USD cap is given in Figure 20.12.
Source: Thomson Reuters Eikon
A floor is used to put a lower level below which the buyer of the option is willing to pay an up-front premium and will be compensated should the interest rates fall below the strike price. Investors who seek a higher interest rate level typically buy floors.
Table 20.7 summarises some of the changes of an option price (premium) for the buyer of the option with the change in various parameters (all other aspects being the same). The table also introduces the Greeks letters used to denote the change of option price with a respective change in each parameter.
A zero-premium option (often inappropriately called a zero-cost option) combines at least one bought option and one sold option, where the total premia of all the bought options is equal to the total premia of all the sold options.
The buyer of the zero-premium option (who has bought and sold options under the structure) pays or receives no premium for the transactions. Similarly, the seller of the zero-premium option receives or pays no premium.
We can use the same example of the call and put options on the GBP USD discussed earlier to construct a popular zero-premium structure called Range Forward (in FX), Collar (in interest rates), and Risk Reversal (generic).
Let the firm, which has to buy GBP (for some payments to be made) against USD, enter a structure for one year, with two components P1 and P2.
Figure 20.13 shows a zero-premium option constructed based on Table 20.8.
As can be seen in the table, above 1.7000, it becomes the right of the firm to buy GBP from the bank at 1.7000 against the USD and thus the option hedges the firm at this level. However, below 1.5000, it becomes the right of the bank to sell GBP to the firm at 1.5000 against the USD (and hence becomes the obligation of the firm to buy GBP against USD). The firm has given up any upside that it would have got (lower GBP USD rate) below 1.5000.
Figure 20.14 presents the payoff diagram.
Various zero-premium structures can be priced—with different payoffs. The same concept of sold options can be used to lower the option premium payable up front. For example, if the structure just discussed were to be repriced and the put option strike was higher, say around 1.2, the premium of the put option will be lower than 1.6%, and the firm will have to pay a net premium of the difference between the two options as an up-front payment.
A vanilla option may be defined as one that has a simple or direct relationship between the difference between the spot and strike at maturity. In contrast, an exotic option is one that has a different kind of payoff profile.
There are two commonly used building blocks for exotic option structures: barrier options and digital options.
Figure 20.15 shows the building blocks of exotic options.
Digital options, as the name suggests, have a digital payout. If an event occurs, the option pays out a predefined amount of money, for which an up-front premium is paid. Digital options are rarely used as stand-alone structures; instead, they are used to add further value to an existing option structure (see Table 20.9).
Condition | Action |
Single touch | Buyer gets paid if a single level is touched (a level either higher or lower than current spot). |
Double touch | Buyer gets paid if either one of two levels is touched (one level is higher and one level is lower). |
Option premium generally is higher than a single touch with a common barrier since the probability of hitting either level is higher than the probability of hitting only one level. | |
Single no touch | Buyer gets paid if the spot remains lower or higher than a single prespecified level (so the buyer starts being in the money). |
Double no touch | Buyer gets paid if the spot remains within a prespecified range. |
Option premium generally is lower than a single no touch with a common barrier since the probability of hitting either level and hence getting knocked out is higher than the probability of hitting only one level. |
Barrier options are those that get triggered, or become invalid, if an event occurs. Like digital options, they are generally used to add further value in existing option structure. Table 20.10 shows barrier option conditions.
Condition | Action |
Knock in (KI) | The option is not live until a particular barrier is hit. Once the barrier is reached, the option becomes live. The premium of this kind of option is lower than the premium of an equivalent vanilla option. |
For a KI option, the closer the barrier is, the higher the price will be. Conversely, the farther the barrier is, the lower the price will be, assuming that the probability of knocking in will be less. | |
Knock out (KO) | The option is live until a particular barrier is hit. Once the barrier is reached, the option expires worthless. The premium of this kind of option is lower than the premium of an equivalent vanilla option. |
For a KO option, the closer the barrier is, the lower the price will be. Conversely, the farther the barrier is, the lower the price will be, assuming that the probability of knocking out will be less. | |
American barrier | This kind of barrier can occur at any time on or before the expiry date of the option. Once the barrier has been touched, the KI or KO conditions get triggered. |
European barrier | This kind of barrier is an observation at the time of expiry. Irrespective of whether the barrier level was touched during the life of the option, if the barrier level has not been touched when the option expires, the KI or KO conditions do not get triggered. |
Up or down | The direction that the spot has to move in order for the barrier to get triggered is denoted by up if the barrier is higher than the spot and down if the barrier is lower than the spot. |
Hence, an up and in call is a call option that gets triggered (KI) when the spot price hits an upper barrier. A down and out put is a put option that gets extinguished (KO) when the spot price hits a lower barrier.
The next example shows how a simple structure can be created using barrier options.
Hence, the firm gets a forward at 1.7000 should the barrier be hit; if the barrier is not hit, it gets spot with a maximum rate of 1.7000.
Firms generally use exotic options in an attempt to decrease the cost of hedging or risk management, achieve a desired rate that is not a forward rate, or obtain a risk profile, return, or structure customised to their view.
Note that the payoffs of exotic options do not guarantee any of the results discussed, and adverse results could cause losses much larger than possible gains from beneficial market conditions. We discuss exotic options further in the case study on derivatives in emerging markets in Chapter 21.
A swap is an exchange of cash flows over time, with prespecified methods of deriving the amount and currency of each cash flow. The basic characteristics of a swap transaction between two parties, A and B, are the descriptions of the two legs—what Party A pays B and receives from B respectively. These are:
In calculating any swap, the forward curve is used to compute the floating rate values of all the applicable legs and to obtain the present value (PV). The rates (spreads in the case of floating rates) at which the PV of both legs is identical is the break-even level of the swap.
The interest rate swap (IRS) is the simplest type of swap and typically is used to move from floating rate to fixed rate or vice versa within the same currency. The corporate payer of the IRS (who pays a fixed rate while receiving a floating rate) typically has a floating rate liability that is to be hedged as a fixed rate or believes that long-term interest rates are going to rise. Figure 20.16 shows a typical IRS. The corporate receiver of a floating rate chooses to diversify borrowings or achieve a targeted hedge ratio or believes that rates (especially the benchmark, such as LIBOR) will move down.
Pricing an IRS with customised dates and requirements, especially in the G7 currencies, is very simple if one has access to a market pricer (see Figure 20.17). In Figure 20.17, USD 500 million floating to fixed IRS has been priced, and the pricing window and the curve used to arrive at that price is displayed here.
Source: Thomson Reuters Eikon
Figure 20.18 shows how the fixed rate is iteratively changed to arrive at the PV of the floating rate. The fixed rate thus arrived at becomes the break-even rate.
Source: Thomson Reuters Eikon
Market information systems, such as Thomson Reuters Eikon, apart from specific pricers shown in the three earlier figures, have pages that display indicative market prices of IRS. An example is shown in Figure 20.19.
Source: Thomson Reuters Eikon
One of the main disadvantages of the payer of the IRS is the opportunity loss if rates stay down or the consequent marked to market () or cash outflow, should the payer be taking on a view or a position.
The coupon swap (see Figure 20.20) is a variant of the simple IRS, where one of the legs is in a different currency. In the example, the firm has a liability in EUR but wishes to convert the interest servicing of the EUR floating coupon into a USD fixed, in order to have more visibility on interest outflow and move it into a currency of choice. The opportunity loss of EUR LIBOR remaining low or moving lower or of possible EUR depreciation (which means fewer USD have to be converted to pay off the same amount of EUR coupon) are two disadvantages of this locking in.
Principal-only swaps (POSs; see Figure 20.21) are used to hedge the currency element of the principal of an asset or liability. In the example, the principal amount of a EUR liability is being hedged through the use of a POS. In effect, the POS is a forward contract with the settlement or exchange of principals happening at today’s spot price; the forward premium or discount takes the shape of coupon cash flows payable periodically through the life of the transaction. Unlike most forwards that have one back-ended exchange at maturity, the POS encourages premium payments over the course of the transaction, thereby making it easier for the hedger POS to time and integrate the coupon payments of the hedge with interest payments on the loan. It also is easier for the hedger to quantify the overall debt burden and get certainty around the principal FX risk—which could be a very large one if the hedger does not have significant EUR inflows, especially back-ended in the final year, as in this case.
If the hedger with a EUR liability wishes to hedge both principal and coupon, we combine the coupon swap with the POS, thereby locking in both coupon and principal payments in USD and fixed amounts. This would provide the hedger with maximum visibility on debt servicing and also eliminate currency risk on the debt payments, given that they do not have large EUR inflows. Figure 20.22 depicts a typical cross-currency swap.
The swaps just described are building blocks for more exotic and structured transactions. Various elements, such as optionality, commodities, equity, and credit, can be built into these swaps to create more exotic and structured payoffs.
The types of swaps discussed earlier should give most treasurers the requisite arsenal on the swap side to solve a large part of their risk management problems that require swaps. Seasoned practitioners with very specific risk views and appetites may use more structured transactions, after having assessed and understood the risk profile and payoffs in detail.
Credit derivatives are one of the largest growing and evolving fields of financial management. Credit markets, as they are now called, are based on finding the price for, and trading, the underlying credit risk in specific instruments or obligors. These markets are closely tied in with fixed income markets, since the underlying tradeable fixed income instruments or assets form the core of credit trading.
When an investor buys a tradeable bond, for example, he or she takes on credit risk. An investor who is long a bond (i.e., owns a bond) is also now the owner of the credit risk associated with the bond (or long the credit risk of the bond); hence, the investor is exposed to the risk (however remote) that the bond issuer will fail to make interest or payments as and when they fall due.
In Chapter 13 the cost of debt for a firm was shown to be a function of:
For purposes of this discussion, we assume that the liquidity spread is zero and that the coupon of a newly issued bond, or the current borrowing rate for the issuer, is benchmark + credit spread.
Figure 20.23 shows us the relationship between the bond and credit risk.
This figure sets us up to delve into the pricing and defeasance of the credit risk.
A credit default swap (CDS) is an exchange of cash flows (swap) on an underlying instrument, asset, or enterprise (reference asset) that gets triggered when there is a default on that asset (credit default), for which a premium is payable (CDS spread).
In effect, a CDS is a derivative contract between two counterparties, whereby the party seeking credit protection (buyer) makes periodic payments to another party providing credit protection (seller) and receives the promise of a predefined amount if a specific issuer (reference entity) defaults. It is akin to an insurance contract on an event happening. In this case, the event is the default of the reference entity or obligor for that asset. In case of default, the buyer of the insurance or the payer of the CDS receives full compensation for the bond or reference asset, while paying back to the seller of the insurance (or CDS) the bond itself a similar bond or the cash equivalent of the bond.
Figure 20.24 depicts how the credit risk of the bond can be synthetically taken out through the CDS.
Effectively, the bank or market maker that is taking on the credit risk of the issuer is getting a return of 3% (equivalent to the credit spread of the issuer) for taking on the risk. This is a simplistic example, and in practice the actual numbers may vary a little, but it puts into context the role and operations of a CDS.
A CDS can be used to hedge existing credit risk or exposure on an entity (provided markets can be made on the credit of that entity). For example, let us say that Firm F has a large exposure to Client C on whose debt CDS trading occurs. If C goes through financial distress, the probability that C will default on its existing debt and its obligations to F are high. F can hedge its credit exposure to C through a CDS if it believes that the risk of default is high. The more in distress the market perceives C to be, the higher the CDS spread or risk premium for insurance the market will charge.
There are multiple ways to embed credit protection into transactions or balance sheets through creative credit structuring. The CDS is the building block for many of these methods. Many books explain the construction, pricing, and workings of the CDS. Readers may want to look into the topic in more depth.
Credit derivatives can be used across different areas:
The important thing to note is that credit transactions tend to require fairly comprehensive documentation and legal checks. A lot of time is required to understand the various elements involved in most structuring activities. Many credit structures also do not qualify for conventional hedge accounting, and treasurers must be well aware of disclosure, valuation, and liquidity aspects and downsides of these transactions prior to entering into them.
The world of products and instruments is large and involved; this book discusses some of the basic building blocks that treasurers and CFOs can use to achieve most financial objectives. To solve complex situations or problems, it is important to keep the solution simple and manageable.