Background on commodity derivatives

Introduction to credit derivatives

BACKGROUND ON COMMODITY DERIVATIVES

Contracts for delivery of commodities at a future date were the pioneers of the derivatives market. The early agreements typically guaranteed the delivery of agricultural products (coffee, cocoa, grain, cotton etc.), nowadays known as ‘soft’ commodities. Present-day derivatives markets typically trade in contracts with energy (oil, gas and related products), bullion (precious metals) and base metals (copper, zinc, aluminium, nickel, lead and tin) as underlying securities. The major exchanges where derivatives are traded are the International Petroleum Exchange (IPE) in London, New York Mercantile Exchange (NYMEX) and Singapore International Monetary Exchange (SIMEX). Energy derivatives are the largest both by market capitalisation and trade volume; hence the sections below will be devoted to their uses and applications.

Exchange-traded commodity futures

Commodity futures are exchange-traded only. They are obligations between two counterparties to take or make delivery of a precisely defined quantity and quality of underlying commodity at the price agreed today at a specified future date. The counterparties may choose to settle the difference between the futures price and the prevailing market price at expiry in cash, rather than opt for physical delivery. The statement above has one major difference compared to the definitions of other futures contacts. The quality as well as quantity of security is precisely defined. As commodities are physical assets, unlike other previously discussed securities, it is vital that both parties understand what is actually being delivered. If an investor was paying for a brand-new BMW to be delivered in the future, he/she would not accept delivery of a run-down Ford Fiesta. Thus the contact specification cannot simply say ’a car’, it has to be precisely defined. However, the quality of most exchange-traded commodities varies from one period to the next, due to natural variability. To try and minimise this variation, energy derivatives allow only a small range of deliverable assets. For example, oil derivatives are based on a small number of crudes, the most widely known being Brent Crude – a mixture from 19 oil fields.

The energy futures market is growing rapidly. At present the amount of futures traded in the market is more than 50 times larger than the level of physical production. This demonstrates how the trading practice changed over the years, from participants wishing to guarantee the price at delivery to those who simply trade for profit.

As with all other futures contracts, energy futures are legally binding agreements to take or make delivery of a specified quantity of a specific product cargo at a future date at a price agreed today on the recognised commodity exchange. The quantity of the product is a multiple of contract sizes specified by the exchange and they are typically cash-settled rather than delivered (if that weren’t the case most of the contracts couldn’t exist, as there simply isn’t enough physical production to fulfil all outstanding obligations). Energy futures have different contract cycle and roll-over dates compared to other futures. There are 12 consecutive delivery months following the present month and the trading ceases at the end of the last business day before the 15th of the month.

At delivery/expiry date the futures contract is settled either by physically delivering the underlying, or the difference between the futures price and the prevailing spot market price is cash-settled. Due to the variation in margin payments, all but the last day’s profits/losses are already incorporated into counterparty positions.

Pricing energy derivatives is extremely complex. Unlike interest rate and equity markets, energy markets respond to an excessive number of factors; from production and usage, extraction and refinement, transfer and storage, to market supply and demand, to name just a few. They are affected not just by economic cycles, but also by seasonality. For example, demand for heating fuel falls in spring and summer, whilst the use of electrical air-conditioners increases. Another important factor is convenience yield. The end users of energy are actually physically burning fuel; they cannot stop their plants and wait around for a better price. Thus energy prices often exhibit premiums in the cash market over the forward market, unobserved in other sectors. The energy derivative prices have to factor in all the characteristics of the underlying commodity as well as the ’usual’ parameters influencing the standard derivative securities. None of the standard quantitative approaches can seamlessly capture the wide range of energy price drivers; hence their valuation is outside scope of this book.

Exchange-traded commodity options

An energy option gives the holder the right but not the obligation to buy/sell an agreed number of energy futures contracts at a price agreed today at or before a date in the future. These are in fact options with an underlying derivative, rather than an asset. A long option position will on exercise result in a long futures position and vice versa. The futures contract, however, will not be taken to expiry; it will be cash-settled immediately. As exchange-traded energy options are American style, most will be exercised or closed out before expiry. The exchange automatically closes out all the remaining open positions. All other properties of exchange-traded options still apply. Pricing energy options is very complex and is outside the scope of this book.

OTC energy swaps

Commodity swaps, or more specifically energy swaps, are the most recent addition to the range of swaps offered OTC. They are a very useful trading tool in commodities markets, as they overcome issues of specific delivery date, relatively short maturities, particular delivery points and quality grades associated with exchange-traded futures.

Energy swaps follow the same principles of other previously discussed swaps. They are contractual obligations between two counterparties to exchange a series of cashflows at regular intervals over a period of time until maturity. Maturities vary to suit clients’ needs, but are typically in the range of one to five years. The cashflows in both legs of the swap are based on an agreed oil index price; one party pays a fixed index rate, whilst the other pays a floating index rate based on monthly average movement of the same index. The exchange of physical assets typically does not take place, but it is possible to construct the swap to allow for delivery. Thus the cashflows are calculated based on a notional quantity of cargo. As with all other swaps, the energy swap is priced so that the present value of both legs is equal at inception, i.e.:

In Chapter 7 on swaps, we saw that pricing interest rate swaps was based on the concept that a swap could be replaced by a strip of futures or FRAs, hence it implicitly had the same value, yielding the single swap rate that would cover the entire strip period. Pricing energy futures is not as straightforward as for their interest rate counterparts, as their underlying price factors are very complex. Thus energy (or other commodity) swap pricing is outside the scope of this book.

INTRODUCTION TO CREDIT DERIVATIVES

Credit derivatives are securities whose value is derived from the credit risk on an underlying asset, rather than the counterparties to the transaction itself. The underlying, also known as a reference entity, is a third party that has incurred debt. Credit derivatives are legally binding contracts between two counterparties whereby one party sells to another protection against the credit risk of the reference entity. The funds are payable following a credit event by one or more third parties.

The buyer and seller specify the credit events that apply to their transaction. Below are some examples:

• Bankruptcy (reference entity becomes insolvent).
• Failure to pay (the third party defaults on one of its obligations, such as a bond or a loan).
• Obligation acceleration (the third party obligation is moved forward in time, e.g. loan repayment is due immediately following the default).

The main users of credit derivatives are banks, hedge funds, insurance companies, pension funds and other corporations. Depending on the type of institution and their requirements, the contracts can be funded (entered into by financial institutions) or unfunded (used both by banks and corporations). Banks typically transact in funded credit derivatives by creating special purpose vehicles (SPVs) that are used to isolate the rest of the institution from financial risk. Payments due on credit derivative transactions are funded through securitisation (debt from various financial institutions is consolidated and resold in tranches as a separate security to other counterparties). Examples of these synthetic structures are collateralised debt obligations (CDOs), credit linked notes, single tranche CDOs, etc. Funded credit derivative transactions are typically rated by rating agencies, allowing the investors to select products depending on their risk-averseness. Under unfunded credit derivatives, both counterparties are responsible for meeting their obligations without resorting to other resources, i.e. each counterparty is exposed to the credit risk of the other. In contrast, under funded derivatives the seller of protection is required to make an initial payment that is used to settle any potential credit events, thus the protection buyer is not exposed to the credit risk of the protection seller.

Examples of unfunded credit derivative products include the following, some of which will be discussed in the subsequent sections:

• Credit default swap (CDS)
• Total rate of return swap (TROR)
• Constant maturity credit default swap (CMCDS)
• Contingent credit default swap
• Dynamic credit default swap
• First to default credit default swap
• Portfolio credit default swap
• Secured loan credit default swap
• Credit default swap on asset backed securities
• Credit default swaption
• Credit spread option (CSO).

Some examples of funded credit derivative products are:

• Credit linked note (CLN)
• Synthetic collateralised debt obligation (CDO)
• Constant proportion debt obligation (CPDO).

Credit default swap (CDS)

The credit default swap (CDS) is the most traded credit derivative instrument. It is a contract between a protection buyer and a protection seller to exchange cashflows in the case of a credit event associated with the debt obligations of a third party (usually a corporation). The protection buyer pays a fixed fee at regular intervals to the protection seller in return for a contingent payment by the seller upon a credit event affecting the obligations of the third party specified in the transaction. The credit events relevant to the transaction are precisely defined and are typically a failure to fulfil obligations or any other event from the list above. If any of these events occur and the protection buyer serves a credit event notice on the protection seller, the seller’s payment is due. If the transaction is cash-settled, the difference between the full face value of the underlying obligation and its current value is paid. In the event of physical settlement, the underlying asset is actually delivered in exchange for its face value (even though its value is reduced). An important difference between CDSs and insurance products is that the protection buyer does not own the underlying obligation. Hence the protection seller has no legal means for recovering losses incurred by payments under the CDS. As the credit derivatives market is growing rapidly, new variations of the above concept are emerging, such as asset-backed securities, discussed in Chapter 12.

Total rate of return swap (TROR)

A total rate of return swap is a contract between two counterparties whereby they swap periodic payments for the period of the contract. Typically, one leg of the swap is based on the total return (interest payments plus any capital gains or losses for the payment period) from a specified reference asset, whilst the other pays/receives a specified fixed or floating cash flow (most commonly Libor + spread). Both legs are based upon the same notional amount.

Akin to equity swaps, the underlying motivation for entering into TRORs is the receiver’s ability to derive financial risks and benefits of an asset without actually owning it. The seller’s view is the opposite; if they believe that the underlying asset is temporarily going to depreciate in value, they use a TROR to stabilise their cashflows and lock in the spread over Libor.

The key difference between a total rate of return swap and a credit default swap is that the CDS provides protection against specific credit events; whilst TROR provides protection from potential losses irrespective of their cause, i.e. it mitigates both credit risk and market risk.

Credit spread swap

A credit spread swap provides protection from smaller downgrades in the credit rating of an underlying asset, rather than outright bankruptcy or default. It is a contract between two counterparties to exchange a series of regular payments, whereby one leg is based on a specific debt issued by a third party (e.g. bond), whilst the other is linked to a comparable government bond with added spread reflecting the difference in credit rating.

At inception, as in all other swaps, the value of the two legs is equal. If the underlying third party debt credit rating changes during the lifetime of the swap, the cashflows are exchanged between the two counterparties.

The motivation for trading credit spread swaps is similar to TRORs, as it allows the investor to lock in the spread over a benchmark yield, whilst providing the buyer with the opportunity for profit in the credit market without direct exposure.

Contingent credit default swap

Contingent credit default swaps are hybrid credit derivatives similar to classic credit default swaps. However, for the contingent payment to take place – in addition to the occurrence of a pre-specified credit event – they typically require a secondary source of credit exposure, i.e. a secondary trigger linked to another reference entity or a movement in interest rates, equity or commodity prices. As the payments are triggered by a joint occurrence of two events, they are less likely to take place compared to the standard credit default swap. Hence they offer less protection and are consequently cheaper. Their valuation is closely linked to the correlation between the two credit events, and the protection is deemed most optimal when the correlation is very low.

Dynamic credit default swap

Dynamic credit default swaps have been introduced to the OTC market to address the issue of uneven credit exposure the market participants are facing, affected by both the passage of time and the underlying market fluctuations. As swap counterparty exposure is a function of market volatility, forward interest rates and time – which in turn can affect the credit rating of the reference entity – having all the variables fixed at the inception of the contract is not ideal. Hence dynamic credit default swaps are tailored to have the notional linked to the mark-to-market value of a reference swap, or a basket of swaps. Thus, the contingent payment, incurred at the time of a credit event, is based on the market value (if positive) of the reference swap, whilst the protection buyer still pays the fixed fee throughout the contract, regardless of the fluctuations in protection provided. Even though the probability of losses to the protection buyer is small – only occurring in the event that both the protection seller and the reference entity default (a very unlikely event if the two are uncorrelated) – the level of protection is still unpredictable as it is contingent on market movements. Hence the protection buyer will typically pay lower fees as compensation.

Constant maturity credit default swap (CMCDS)

A constant maturity credit default swap (CMCDS) is similar to a standard credit default swap (CDS). Under a CMCDS contract, the protection buyer makes regular premium payments to the protection seller, and in return receives a payoff contingent on the credit event of an underlying financial instrument. In contrast to the standard CDS, the premium leg of a CMCDS is not fixed at the inception of the contract; instead it is a floating spread, using a traded CDS as a reference index. Specifically, given a pre-agreed time to maturity, each premium payment is equal to a spot CDS spread on the same reference credit (with the same time to maturity) traded in the market. The default or protection leg is typically structured in the same way as the standard CDS (i.e. the same contingent credit events apply). Comparison between the CDS and CMCDS is akin to the relationship between the fixed and the floating interest rates, whereby the former is known at the outset, but might hurt the borrower should the rates rise. Similarly, the purchaser of the CDS has obtained credit protection at a fixed cost, whilst the CMCDS buyer is exposed to market credit risk fluctuations. The choice between the two depends entirely on the type of investor and their view of the credit market.

First to default credit default swap

First to default swaps are typically used by investors aiming to increase yield on investment, rather than as credit protection vehicles. In this case the investor is the buyer of the risk, rather than risk protection. The risk buyer thus takes a position in each risk-bearing asset proportional to the notional sum invested. Throughout the swap the buyer receives coupon payments until occurrence of the first credit event. In the event of the first credit default (or other pre-specified contingent event), the investor no longer bears the risk of the credit entity. Depending on the specification, the contract is either immediately terminated, or carried forward until maturity. In either case, the losses incurred by the credit default (payable by the risk buyer) are equal to the difference between the par value and the final price of the reference entity. This is a very complex product, as credit assessment and probability of default are hard to predict, the timing of credit events even more so. However, these are attractive products that offer potential substantial yield enhancement. Their concept is further extended to capture second to default, third to default, or more generally n^th to default, hence the investor can specify which credit event their investment is linked to.

Credit spread option (CSO)

Even though all types of option contracts are available, the most popular credit spread option is the put option on an asset swap. The motivation behind such a contract is the option buyer’s view that the credit spreads would widen. In such an event the bank would purchase a put option to deliver an asset (e.g. bond) at some future date. The strike is expressed as yield, rather than price (e.g. Libor + 50). The option will be exercised only if the bond yield is above Libor + 50, i.e. the bond price is lower than the original value. The bank will make a profit by selling the bond for more than it is worth.

Pricing credit derivatives

Credit derivatives valuation is a very complex issue, due to many unobservable price factors and the complexity of the traded products. Whilst interest rate derivatives have most of their price drivers directly observable in the market, predicting a bankruptcy of a particular corporation and translating it into a mathematical equation does not come easily.

A model used to price the risk of default at the minimum needs to incorporate (implicitly or explicitly): default probability, severity of loss given a credit event has occurred, timing of such a credit event and recovery rates (as the reference entity has defaulted, the amount recovered is contingent on many market and legal aspects). Another important issue is related to the model input parameters. In most other classes of derivative products, the liquidity and price transparency is such that it easily provides accurate and timely model parameter values. Due to the complexity of credit derivatives, market practitioners typically resort to making assumptions. This is due to the so-called ‘dual observation issue’, whereby the market-observed credit spreads can imply the severity of loss given default, but this data can only be used if an assumption is made about the likelihood of default. Hence the credit derivative pricing is a joint issue of market data validity and the sophistication of the pricing models.

There are two main approaches to pricing credit derivatives: numerical (probability model) and analytical (arbitrage-free) model. The parameters they have to incorporate are much more complex than those used by other markets. Hence the pricing of credit derivatives is outside the scope of this book.