Derivatives. Synopsis. 1. Introduction. Learning Objectives

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1 Synopsis Derivatives 1. Introduction Derivatives have become an important component of financial markets. The derivative product set consists of forward contracts, futures contracts, swaps and options. A key issue is how prices for such derivatives are determined. The ability of market participants to set up replicating portfolios ensures that derivative prices conform to no-arbitrage conditions. That is, the prices cannot be exploited without taking a risk. Replication also explains how derivative claims can be manufactured to order. The principal justification for the existence of derivatives is that they provide an efficient means for market participants to manage risks. But derivatives also have other uses such as speculation and the implementation of investment strategies. After completing this module, you should: know the history of the development of derivatives, namely that: there is early historical evidence for forward and option contracts futures contracts were developed in the 19th Century and that financial futures were introduced in 1973 swaps were first traded as recently as 1981 new derivative products continue to be developed to meet specific needs of market participants know that derivatives are designed to manage risk, usually the price or market risk of the underlier that arises from uncertainty about the underlier s value in the future. In particular, that: market participants who need to buy in the future are exposed to the risk that prices may rise before they can buy. This exposure to price risk is known as buyer s risk market participants who need to sell in the future are exposed to the risk that prices may fall before they can sell. This exposure to price risk is known as seller s risk be able to differentiate between the different elements of the risk management product set, namely forward contracts, futures, swaps, and options; understand how prices in financial markets are maintained in proper relationship to each other through arbitrage; be aware that arbitrage relationships rely on the Law of One Price and how imperfections in the way real markets operate can limit the applicability of the law; understand that the payoff of derivative instruments can be replicated using combinations of fundamental financial instruments; understand how in an efficient market the prices of derivatives, which can be replicated using fundamental financial instruments, are determined through arbitrage-free relationships;

2 know the main uses for derivatives, namely: risk modification hedging speculation spreading arbitrage lowering borrowing costs tax and regulatory arbitrage completing the market be aware that the main justification for derivatives is that they enable market participants to efficiently transfer risks. 1.1 Introduction 1.2 Arbitrage Relationships 1.3 Derivative Markets 1.4 Uses of Derivatives Derivatives are contracts specifically designed to manage risks. Although technically redundant securities since they can be replicated using fundamental financial instruments, they provide an efficient means for market participants to manage and transfer risks. Their importance in this role continues to increase and they have become an important element in modern financial markets. While some, such as futures and swaps, are relatively new classes of instruments others such as forward contracts and options have always been a feature of commercial life. The great expansion over the last 30 years or so in derivatives on fundamental financial instruments is due to changes in the financial system and theoretical developments in our understanding of how these instruments can be valued. A key principle of valuation in an efficient market is the ability of replicating portfolios made up of fundamental financial instruments to provide the same payoffs as derivatives. Under the Law of One Price, two assets or combinations of assets with the same payoffs should have the same price. This identity between the derivative contract and a replicating portfolio with the same payoffs as the derivative is enforced by arbitrage. While this theoretical understanding provides the ability to price derivatives, frictions in real world financial markets may lead to divergences between theoretical arbitrage-free prices and actual market prices for derivatives. Derivatives are traded either on organised exchanges with specific rules and a significant degree of investor protection or directly between market participants in the over-the-counter markets. In the later case, market participants have to take into consideration the credit risk of the counterparty to the transaction. Exchange-traded contracts have standardised terms and conditions, OTC derivatives can be customised as required. Derivatives provide market participants with not just the opportunity to modify risks, but also to engage in speculation and to undertake transactions that would otherwise be problematical when undertaken using fundamental financial instruments. These include such benefits as reducing financing costs and taking advantage of tax benefits and regulations.

3 2. The Derivatives Building Blocks This module introduces the derivatives product set and shows how the individual products are related. It discusses the two principal kinds of products used to manage financial risk: terminal instruments and options. It follows a building-block approach to show how the different instruments, forward contracts, futures contracts, swap contracts and options, have common fundamentals. The key differences for terminal products relate not so much to their economic effects, which are remarkably similar in that their gains or losses are directly related to the underlying asset price, but to the way the different instruments handle performance risk. With a forward and a swap contract, each party is directly taking the counterparty risk of the other. This is not the case with futures where contracts are collateralised and an intermediary institution, the clearing house, acts as guarantor. Options have a non-linear function in relation to the underlying asset price and the position of the two sides to the option transaction is very different. The option buyer has performance risk with the option seller, but the seller has no risk in regard to the buyer since the buyer will only exercise his right to perform if it is to his advantage to do so. Although options appear to be radically different instruments from the terminal products, it is shown that this is not the case and that options can be seen as being made up of a package consisting of a forward contract and a loan. After completing this module, you will understand: how terminal contracts are put together; how options modify the underlying risk profile of a position; and how to apply a building-block approach to derivatives. 2.1 Introduction 2.2 Forward Contracts 2.3 Futures Contracts 2.4 Swap Contracts 2.5 Option Contracts This module introduces the basic elements of the derivatives product set and illustrates how the building blocks relate to each other. The financial markets are replete with different products which are baffling to an outsider. Does an exchange of differences differ from a forward outright transaction, or a currency option from the call provision in a bond? These are just some of the complexities that must be dealt with if one is to understand financial markets. Examination reveals, however, that seemingly complicated instruments are similar if not the same in terms of what they do.

4 The product set can be broken down into two parts. First, there are the terminal products. These are made up of various kinds of forward contracts, which are bilateral agreements between market participants and which are subject to counterparty risks. Next are futures, which differ from forwards in that the contract is effectively renegotiated each day at the new prevailing market rate. When this approach is used, futures virtually eliminate credit risk or performance risk, which is the major disadvantage of forward contracts. Finally, there are swaps, which involve intermediate payments over the life of the contract and which are equivalent to a bundle of forward contracts. The other building block of the financial derivatives product set consists of options. These come in two basic kinds, an option giving the right to buy, known as a call, and an option giving the right to sell, known as a put. Although options offer a one-way bet on the future outcome, they can be characterised as being a package made up of a forward contract and a loan. 3. The Product Set: Terminal Instruments I Forward Contracts Terminal contracts are of three kinds: forwards, futures and swaps. The least complicated is the forward contract, which is a bilateral agreement between two parties. The key determinant of the pricing of terminal instruments is through hedging. This module and Module 4 on futures examine the nature, structure and risks of simple terminal contracts. Module 5 looks at swaps, which can also be seen as packages of forward contracts. The other member of the derivatives product set consists of options (which are discussed in Modules 6 10). This module examines the nature and use of forward contracts to hedge risks. Forward contracts are the simplest of the terminal instruments used to manage various kinds of risk and, because they can be tailored to specific user needs, they provide a perfect hedge. The forward contract form has been adapted to address the problem of credit risk (or default) on such deferred-performance contracts and two examples are shown: the forwardrate agreement, for interest rates, and the synthetic agreement for forward exchange, for currencies. After completing this module you should: be able to price a forward contract; know how specific forward contracts work in currencies and interest rates; understand the credit risk implications of the forward contract; understand how modifying the contractual cash flows reduces credit exposure. 3.1 Introduction 3.2 The Nature of the Forward Contract 3.3 Using Forwards as a Risk-Management Instrument 3.4 Boundary Conditions for Forward Contracts 3.5 Modifying Default Risk on Forward Contracts

5 Forward contracts exist on a great range of different financial instruments and commodities. They are transacted between firms in the over-the-counter markets, are bilateral agreements and can be modified to meet both parties needs. This inherent flexibility in relation to terms and conditions makes them very useful instruments. The basic model for valuing a forward contract is the cost-of-carry model. This might equally be called the pricing through hedging model since it is based on the net cost of eliminating the price risk by the seller of the contract. For most forward contracts this will be the net funding costs associated with holding the underlying asset, plus some storage, and other ancillary costs. In situations where storage and other costs are virtually zero, as with financial instruments, the cost-of-carry model is simply the net interest-rate cost over the contract period to the future delivery. The attraction of the forward contract as a risk-management instrument is that it provides a simple way of eliminating future uncertainty on the price or rate at which a transaction can be made at some point in the future. Whereas the tailored nature of the forward is very advantageous, the fact that it is a bilateral agreement means that both parties to the contract have counterparty risk on the other. This makes forward contracts credit instruments with all the disadvantages that these entail. Variations on the basic forward have been developed to reduce the credit element on such contracts. Two examples, the forward-rate agreement (FRA) and the synthetic agreement for forward exchange (SAFE), show how an instrument can be developed which mitigates credit risk. The FRA is a useful instrument for eliminating interest-rate risk. The SAFE group of instruments provide an equal structure between two currencies, the ERA being an instrument that protects against movements in the forward points, or interest-rate differential; while the EXA has the same exposure as a forward-start foreign-exchange swap. The latter instrument makes it more useful in hedging currency risk, but without the same degree of counterparty exposure that is inherent in a conventional swap contract. Of course, intermediaries have other ways of controlling credit risk, for instance, by requiring the other party to post a surety or performance bond (collateral). Such an approach will be looked at in the context of the futures contract, which forms the basis of the next module. 4. The Product Set: Terminal Instruments II Futures This module continues the examination of the nature and use of terminal products by looking at the second type of basic derivative, namely futures. Terminal contracts are of three kinds: the simplest is the forward contract, already discussed in Module 3, which is a bilateral agreement between two parties; the futures contract is an exchange-traded contract which has many of the features of a forward contract but is designed to eliminate, to a large extent, the credit-risk element that exists in forwards. The key determinant of the pricing of all the terminal instruments is through hedging or the cost-of-carry model.

6 After completing this module you should: be able to price a futures contract; understand the technical differences between a forward contract and a futures contract; know how specific futures contracts work in currencies and interest rates; understand the effects of the basis on a futures price; know what is meant by backwardation and contango in futures prices; know what convergence means and how it affects the futures price over time; know the limitations involved with futures contracts for hedging purposes. 4.1 Introduction 4.2 Futures Contracts 4.3 Types of Futures Transactions 4.4 Convergence 4.5 The Basis and Basis Risk 4.6 Backwardation and Contango 4.7 Timing Effects 4.8 Cash Futures Arbitrage 4.9 Special Features of Individual Contracts 4.10 Summary of the Risks of Using Futures This module has examined the institutional and market arrangements used for futures. The great advantages of futures over forward contracts are their liquidity, low transaction costs and the role of the exchange in addressing specific counterparty risk problems. Liquidity is achieved through standardisation of contract specifications. While the advantages of futures derive from their institutional arrangements, these same structures also lead to their disadvantages. Futures contracts are inflexible, leading to hedge inexactness, a problem known as basis risk. The margining systems lead to intervening cash flows which require the hedger to monitor the position and, possibly, to make adjustments to the hedge. Consequently, there are trade-offs between the benefits of a traded market and contract specificity, between virtually eliminating counterparty risk and assuming credit risk and between cost and continual monitoring of positions. Functionally, forwards and futures achieve the same result. The judgement as to which to use is as much part of the riskmanagement task as is the decision to hedge or live with the exposure. 5. The Product Set: Terminal Instruments III Swaps This module looks at the third category of derivative terminal instrument: the swap. Such an instrument is more complex than the single-date structures of forwards and futures. Following their invention, a large number of different swap types have been developed in

7 response to market needs, although the two principal kinds relate to cross-currency and interest-rate swaps. A swap contract has many of the features of a term instrument, such as a bond, but equally it can be unbundled into a portfolio of simple forward contracts for pricing and risk-management purposes. The credit risks of interest-rate swaps are far less than the equivalent risks of holding a bond. This is not true of a cross-currency swap, where credit risk increases with the time to maturity. As a liability-management instrument, swaps provide an effective means for borrowers to exploit their comparative advantage in particular markets while at the same time maintaining their desired exposure profile to interest rates and currencies. Swaps therefore enable borrowers to manage position risk rapidly and at minimum cost. As an asset-management instrument, they offer the same attractions as for liability management, namely, exploiting anomalies and rapidly managing position risk at minimum cost. Swaps allow asset liability managers to alter their overall exposure to a particular currency or interest rate without having to undertake the early repayment of outstanding borrowings or to realise investments. Swaps also facilitate cash-flow management. After completing this module, you should know: the nature of the different types of swaps; how swaps are used for risk modification, asset liability management and arbitrage across markets; how to price a new, or at-market, swaps contract; how to value or unwind an existing, or seasoned, swaps contract; the credit exposure on swaps. 5.1 Introduction 5.2 Interest-Rate Swaps 5.3 Cross-Currency Swaps 5.4 Asset Liability Management with Swaps 5.5 The Basics of Swap Pricing 5.6 Complex Swaps 5.7 The Credit Risk in Swaps Swaps are the newest instrument in the derivatives product set. Whereas forwards and futures hedge a single cash flow, swaps hedge a series of periodic cash flows. From an initial start in the early 1980s they have established themselves as a very important building block in managing various kinds of market risks. The swap mechanism provides a very flexible way of altering the nature of a set of cash flows, either in terms of their interest-rate exposure or currency, or both. The development of swaps has provided linkages between different markets, thus allowing participants to exploit advantages and arbitrage opportunities. Swaps are extensively used by asset and liability managers to control risks and to exploit anomalies in the capital markets. By combining simple swaps, it is now possible to create complex packages which provide tailored solutions to many risk-management problems. Swaps need to be carefully valued using a term-structure approach. At inception, an atmarket swap (ignoring transaction costs) will have a zero net present value, after any

8 adjustments. As the swap moves towards maturity it will become off-market and may become an asset or a liability. Depending on the path of interest rates, it may be subject to credit risk. Calculating the potential loss from a swap default requires two things to happen simultaneously: the swap must be an asset and the counterparty must also default. 6. The Product Set II: The Basics of Options This module introduces options, the terminology used in describing options and how they are used to modify the risk profile of a given position. One of the complexities with options is the specialist language used to describe them. The basic factors which affect option values are shown with a simple example and the boundaries to the value of options are then explained. The module finishes with a discussion of how options can be used to modify the risk profile of a given exposure. After studying this module, you should understand: the options terminology; the basic option-pricing variables; how options are used to modify risks; the boundary conditions for the values of options. 6.1 Introduction 6.2 Types of Options 6.3 Option-Pricing Boundary Conditions 6.4 Risk Modification with Options This module introduced the basic character of options. Options are somewhat technical in nature, but the technical aspect relates partly to the specialised language used to describe options and partly to the mathematical nature of the discussions related to pricing. These are discussed in the next two modules. There are two basic kinds of option: calls, which give the right to purchase an asset, and puts, which give the right to sell an asset. The risk taken by the buyer or holder is very different from that taken by the seller or writer. In both cases, the writer is potentially exposed to a large loss if the price of the underlying asset moves against him or her. Thus there is an asymmetrical or non-linear payoff. Options change their character depending on whether they are in- or out-of-the-money, the value of an out-of-the-money option being purely the probability that the option will have some value at expiry. An in-the-money option, however, has many of the characteristics of a deferred purchase, or sale, of a terminal instrument. This dualism has contributed to difficulties in understanding their nature. This module has shown that option values relate to a number of pricing factors, namely, the asset price, the strike price, the life or time over which the option is granted, the

9 prevailing interest rate, whether there are any distributions from the underlying asset over the option s life and the asset s volatility. These pricing variables have a different effect on the value of calls and the value of puts. Because options allow the holder to modify favourably the risk exposure of a given asset, they are valuable. As a consequence buyers have to pay an upfront premium. But they also have the unique feature of allowing the holder to walk away from the contract. In addition, there are minimum price boundary conditions which apply to their value. The ability to modify risk is a very useful attribute, which makes options of particular value to the investor or risk manager. 7. The Product Set II: Option Pricing This module introduces methods for valuing options. The value of an option is merely the present value of its expected payoffs. If these can be established for a one-period case, then the value of the call is easily derived. Option pricing is based on pricing through hedging the exposure created by the option seller (or writer). After completing this module, you should: understand how the hedging or replicating portfolio approach is used to value an option; understand the role of the replicating portfolio in option pricing; know how to derive a fair value for an option; be able to price an option using a discrete time binomial method; know how the option s hedge ratio, or delta, is derived; be able to use the put call parity relationship to price the corresponding put option. 7.1 Introduction 7.2 Pricing the Option Liability 7.3 Multiperiod Extension of the Option-Pricing Method 7.4 Put Call Parity Theorem for Pricing Puts This module has looked at a formal model for pricing call options. It is based on a discrete time method where the asset value can take only one of two states, either an increase or a decrease. Given information about the asset s future price behaviour, it is possible to price the option. The value of a call option at expiry will be the difference between the asset price and the strike price if that is positive (that is, {max. }). The liability that the option writer is obligated to deliver is valued through creating a portfolio of the underlying and borrowing which exactly matches this, the residual cost of setting up this position being the amount that the option buyer or holder has to pay for the transaction to be fair to both sides. The

10 fair value of an option is thus derived from the ability of the option writer to create a suitable replicating portfolio. A put option can be valued by using the put call parity theorem to price a corresponding put from the call. Module 8 will extend the analysis of Module 7 and will examine an analytic solution to the problem of option pricing that does not require a large number of calculations. This involves a continuous time model first developed by Fisher Black and Myron Scholes. 8. The Product Set II: The Black Scholes Option-Pricing Model This module extends the option-pricing method to provide an analytic solution to the value of calls and puts using the Black Scholes option-pricing model. After completing this module, you should know how: the Black Scholes option-pricing model equation works; to calculate the inputs used in the model; to use the put version of the Black Scholes model. 8.1 Introduction 8.2 The Black Scholes Option-Pricing Formula for Calls 8.3 The Black Scholes Option-Pricing Formula for Puts 8.4 Properties of the Black Scholes Option-Pricing Model 8.5 Calculating the Inputs for the Black Scholes Option-Pricing Model 8.6 Using the Black Scholes Option-Pricing Model This module has introduced an analytic method for pricing options, the well-known Black Scholes option-pricing model. The advantage of this analytic approach is that it provides an exact closed-form equation for pricing the option rather than requiring the iterative method of the binomial model. That said, both models if used correctly provide a close result, especially if a large number of steps are used for the binomial tree. Nevertheless, the attraction of the Black Scholes model is that it is easy to use, requiring a simple hand calculator and a set of tables giving the ordinates under the normal distribution. Because of these and other advantages, the model will be used in Module 10 which extends the approach to assets other than the non-dividend-paying stock for which it was originally developed. The Black Scholes model also allows the user to calculate useful sensitivity measures, known colloquially as the Greeks of option pricing, for measuring the effects of changes in one of the pricing variables on the value of the option. These effects are discussed in the next module.

11 9. The Product Set II: The Greeks of Option Pricing Options have complex behaviour. This is due to the multidimensionality of the pricing variables involved. In order to understand option behaviour it is necessary to know how they respond to changes in the value of the pricing factors. The sensitivity of the option price to changes in the pricing factors is colloquially known as the Greeks of option pricing. This is because these value sensitivities to changes in one of the pricing variables, derived from the option pricing model, are characterised by Greek letters of the alphabet. The key Greeks of option pricing are delta, gamma, rho, theta and vega. Delta measures the sensitivity of option price to changes in the price of the underlying asset. Gamma shows the rate of change in the option delta. Rho is the option sensitivity to changes in interest rates; theta is the sensitivity of the option to time decay; and vega, the sensitivity to changes in volatility. After completing this module, you should understand: the multidimensional character of options; how sensitive option values are to changes in each of the pricing factors; the importance of delta, gamma, rho, theta and vega as measures of option-price sensitivity; how values respond over the life of the option; the use of option sensitivities in structuring option strategies within a market view. 9.1 Introduction 9.2 The Effect on Option Value of a Change in the Pricing Variables 9.3 Sensitivity Variables for Option Prices 9.4 Asset Price (U0) and Strike Price (K) / Delta (δ), Lambda (λ) and Gamma (γ) 9.5 Option Gamma (γ) 9.6 Time to Expiry / Theta (θ) 9.7 Risk-Free Interest Rate (r) / Rho (ρ) 9.8 Volatility (σ) / Vega (ν) 9.9 Sensitivity Factors from the Binomial Option-Pricing Model 9.10 Option Position and Sensitivities The change in option value for a change in one of the pricing variables depends on whether the option is a call (the right to buy) or a put (the right to sell). In order to understand options, one must understand the effects of such changes. The five key factors which go to make up an option s value are the price of the underlying asset, the strike price, the time to expiry, the risk-free interest rate and the asset s volatility. Using an option-pricing model, it is possible to derive one or more sensitivity factors which measure how the option s value changes in response to changes in one of the pricing factors. The key sensitivities derived from such a model are delta, gamma, theta and vega which respectively measure the option s sensitivity to changes in the underlying asset s price, the risk in delta, the effect of time and

12 the volatility risk of the option. Of the pricing factors, option value is most sensitive to changes in volatility. In addition, an option s sensitivity to the pricing factors will change in complex ways due to interactions between the various factors. Option behaviour is asymmetric and follows complex paths, depending on what is happening to the various variables. Behaviour will depend, for instance, on whether the option is out-of-the-money, at-the-money or in-themoney. Examining the sensitivity factors shows that, generally speaking, options which are near-to or at-the-money are more susceptible to value changes than options at either extreme. Equally, options which are near to their expiry date are usually more sensitive to changes in the pricing factors than options with a longer remaining life. Given an understanding of how an option behaves in respect to changes in one of the pricing variables, a position can be established which provides the right sensitivity to expected changes in the variable. Understanding the effect of such sensitivities also allows the undesirable effect to be hedged out by establishing the appropriate opposing position. In some cases this involves taking the appropriate position in the underlying asset. For some kinds of option risks, however, it is necessary to offset these with other positions in options since only options provide the requisite price behaviour. Managing options is, therefore, a complex operation. This complexity is increased by the need to manage the position over time since changes in the pricing variables will change the position s sensitivity and frequent rebalancing is likely to be required. 10. The Product Set II: Extensions to the Basic Option-Pricing Model This module looks at how the basic option-pricing model can be expanded to include options on classes of instruments with different behaviour characteristics. It also discusses the adjustments required to value American-style options where there is the possibility that it is more profitable to exercise the option before expiry. The module also looks at exotic options which modify one or more of the standard features of traditional options. Most of the adjustments to the model are not complicated once the logic of the change is understood and involve only minor alterations to the basic pricing equations. That said, interest-rate options create some special problems in pricing given the special characteristics of interest-rate-sensitive assets. After completing this module, you should know how to price options when: there is a value leakage in the form of dividends or interest payments; the option is on an exchange rate between two currencies; the option allows the holder to lock in an interest rate; there is the possibility of early exercise, as is the case with American-style options; and you should understand: the complexities of pricing interest-rate options.

13 10.1 Introduction 10.2 Value Leakage 10.3 Value Leakage and Early Exercise 10.4 Interest-Rate Options (IROs) 10.5 Complex Options Although the original Black Scholes model was developed to price European-style options on non-dividend-paying stocks, it has proved possible to adapt the model to take account of the characteristics of different types of assets. Some of these adjustments are relatively straightforward, such as including the effect of value leakage dividend or interest payments on the option value. Other adaptations require a more complex solution, the aim of which is to preserve the simplicity of obtaining an analytic solution to the value of an option rather than to resort to the iterative numerical procedures of the binomial model. Only when a relatively easy adjustment cannot be made to the Black Scholes equation must the user resort to numerical procedures. In terms of providing an extension to the original Black Scholes model, interest-rate options have been, and remain, an asset class where simple solutions have proven to be most problematical. The existing models are complex to operate and, in most cases, make somewhat unrealistic assumptions about the underlying term structure. That said, Black s version of the analytic model provides a generally adequate method of valuing options on short-term interest-rate-sensitive assets with simple cash flows. For bonds, the Schaefer Schwartz correction to Black s equation is a simple way of adjusting for the declining volatility of a bond as it moves towards maturity. More complex interest-rate-option models have been developed to price options on interest-rate-sensitive assets which make use of the term structure. This remains an area of continual development and refinement. Finally, the changes made to the nature of options themselves and the growth of options with special features collectively known as exotic options are briefly outlined to show how instruments and products are continually evolving in response to the needs of market participants and the resourcefulness of financial engineers. A detailed analysis of these exotica is beyond the scope of this module. 11. Hedging and Insurance This module looks at how risk is managed through hedging and insurance. The basic principle of hedging is straightforward. It is to match two opposing sensitivities in such a way that value changes on both sides of the position cancel out. The problem arises when the two positions do not change in value in exactly the same way, leading to an imperfect correlation of price behaviour. The greater the divergence in the two sides in terms of their underlying characteristics, the greater the degree of hedging risk. A cross-asset hedge will be

14 imperfect, whereas a customised forward contract will provide a perfect hedge. Various methods for determining the optimal hedge when the two sides differ are discussed. Options are used to provide insurance: they protect the holder against the undesirable outcomes, while leaving the user the opportunity to profit from the favourable ones. After completing this module, you should know how to: set up a hedge; create an optimal hedge position; determine a cross-hedge; understand the effect of basis risk on a hedged position; hedge against a rotational shift in the yield curve; manage risk via dynamic hedging; make use of options in a hedging strategy Introduction 11.2 Setting up a Hedge 11.3 Hedging Strategies 11.4 Portfolio Insurance 11.5 The Use of Options as Insurance Hedging is an essential tool for risk management. It is an approach that involves creating an appropriate portfolio where the hedge position offsets the exposure. As an alternative, the insurance approach involves acquiring protection against undesirable movements in the source of risk. Derivatives provide the simplest way in which to undertake these transactions. Whereas terminal instruments are essentially free, options involve upfront costs but also provide a greater element of flexibility in hedging risk. Indeed for some kinds of exposures, they provide the only satisfactory approach to the problem. Options are uniquely useful in providing insurance against contingent exposures and in providing a floor to potential losses. As with all insurance decisions, the level of cover and whether insurance is required depends on individual preferences. The use of derivatives can create some problems. With a perfect hedge, the value changes of the position and the derivative exactly offset each other. When the hedge is less than perfect, basis risk arises. What the module demonstrates is that, in addition to understanding how the various derivative instruments are priced, it is also necessary to understand how they can be applied as risk management tools. An effective use of derivative instruments to manage risk requires setting up the hedging transaction so as to neutralise a large part of the change in value of the cash position. To find the least-risk hedge, the minimum variance hedge ratio provides the best combination of asset and hedge that minimises the value divergence (or basis risk) between the two. The module also shows that the market for derivative instruments also affects how they can be used. The need to use a stack hedge is the result of a lack of liquidity or the nonexistence of longer-dated contracts. Also it is necessary to understand how the instruments

15 will behave as market prices change. This makes an understanding of these issues an integral part of understanding derivatives. With options special factors apply. For a start when used for risk management purposes they need rebalancing and monitoring since the insurance benefit they provide changes as market conditions change or as the contracts move towards expiry. Finally, an understanding of how derivatives work allows a market user to develop innovative solutions to investment and risk management problems. Portfolio insurance makes use of key understandings about the behaviour of options and how to manage their risk. 12. Using the Derivatives Product Set This module integrates the different elements of derivatives and the use of the derivatives product set discussed in earlier modules. In particular, it shows how the risk manager uses the various instruments to manage exposures. The examples are based on managing foreignexchange-rate risk and commodity price risk, but the process is equally applicable to the other types of market risk. After completing this module, you should understand: how the initial position and the appropriate hedge are determined; some of the issues relating to the appropriate instruments to be used; the difference in payoffs between terminal instruments and options; how risk management can be used to modify the unacceptable features of firms projects Introduction 12.2 Case 1: British Consulting Engineers 12.3 Case 2: United Copper Industries Inc. This module has looked at two case studies of risk-management activity. The first covers the different approaches used to manage the currency risk in a future foreign currency receivable. The second, more complicated case looks at the issues surrounding the commodity price risk associated with a major capital investment project and different approaches that might be used to manage the risk.