18.1 Introduction to derivative markets and instruments

  • Introduction
  • Types of derivatives: forward commitments; contingent claims
  • Overview of derivative markets; regulation, players
  • The purposes of derivative markets
  • Criticisms of derivative markets
  • Elementary principles of derivative pricing

18.2 Forward markets and contracts

  • Introduction: Delivery and settlement of a forward contract; default risk and forward contracts; termination of a forward contract
  • The structure of global forward markets
  • Types of forward contracts: equity forwards; bond and interest rate forward contracts; currency forward contracts; other types of forward contracts
  • Pricing and valuation of forward contracts: generic pricing and valuation of a forward contracts; pricing and valuation of equity forward contracts; pricing and valuation of fixed- income and interest rate forward contracts; pricing and valuation of currency forward contracts
  • Credit risk and forward contracts
  • The role of forward markets

18.3  Futures markets and contracts

  • Introduction: brief history of futures markets; public standardised transactions; homogenisation and liquidity; the clearinghouse; daily settlement; and performance guarantee; regulation
  • Futures trading: the clearinghouse, margins, and price limits; delivery and cash settlement; futures exchanges
  • Types of futures contracts: short-term interest rate futures contracts; intermediate- and long- term interest rate futures contracts; stock index futures contracts; currency futures contracts
  • Pricing and valuation of futures contracts: generic pricing and valuation of a futures contract; pricing interest rate futures, stock index futures, and currency futures
  • The role of futures markets and exchanges

18.4 Risk management applications of forward and futures strategies

  • Introduction
  • Strategies and applications for managing interest rate risk: managing the interest rate risk of a loan using an FRA; strategies and applications for managing bond portfolio risk
  • Strategies and applications for managing equity market risk: measuring and managing the risk of equities ; managing the risk of an equity portfolio; creating equity out of cash; creating cash out of equity
  • Asset allocation with futures: adjusting the allocation among asset classes: pre-investing in an asset class
  • Strategies and applications for managing foreign currency risk: managing the risk of a foreign currency receipt; managing the risk of a foreign currency payment; managing the risk of a foreign-market asset portfolio

18.5 Swap markets and contracts

  • Introduction: characteristics of swap contracts; termination of a swap
  • The structure of global swap markets
  • Types of swaps: currency swaps; interest rate swaps; equity swaps; commodity and other types of swaps
  • Pricing and valuation of swaps; equivalence of swaps and other instruments; pricing and valuation
  • Swaptions: basic characteristics of swaptions; uses of swaptions; swaption payoffs; pricing and valuation of swaptions
  • Forward swaps
  • Credit risk and swaps
  • The role of swap markets

18.6 Risk management application of swap strategies

  • Introduction
  • Strategies and applications for managing interest rate risk: using interest rate swaps to convert a floating-rate loan to a fixed-rate loan (and vice versa); using swaps to adjust the duration of a fixed-income portfolio; using swaps to create and manage the risk of structured notes
  • Strategies and applications for managing exchange rate risk: converting a loan in one currency into a loan in another currency; converting foreign cash receipts into domestic currency; using currency swaps to create and manage the risk of a dual-currency bond
  • Strategies and applications for managing equity market risk; diversifying a concentrated portfolio; achieving international diversification; changing an asset allocation between stocks and bonds; reducing insider exposure
  • Strategies and applications using swaptions; using an interest rate swaption in anticipation of a future borrowing; using an interest rate swaption to terminate a swap;

18.7 Option markets and contracts

  • Introduction
  • Basic definitions and illustrations of options contracts: basic characteristics of options; some examples of options; the concept of moneyness of an option
  • The structure of global options markets: over-the-counter options markets; exchange-listed option markets
  • Types of options: financial options; options on futures; commodity options; other types of options
  • Principles of option pricing; payoff values: boundary conditions; the effect of a difference in exercise price; the effect of a difference in time to expiration; put-call parity; American options, lower bounds, and early exercise; the effect of cash flows on the underlying asset; the effect of interest rates and volatility; option price sensitivities
  • Discrete-time option pricing: the binomial model; the one-period binomial model; the two- period binomial model; binomial put option pricing; binomial interest rate option pricing; American options: extending the binomial model
  • Continuous-time option pricing: the Black-Scholes-Merton model; assumptions of the model; the black-Scholes-Merton formula; inputs to the black-Scholes-Merton model; the effect of cash flows on the underlying; the critical role of volatility
  • Pricing options on forward and futures contracts and an application to interest rate option pricing: put-call parity for options on forwards; early exercise of American options on forward and futures contracts; the black model; application of the black model to interest rate options
  • The role of options markets

18.8  Risk management applications of option strategies

  • Introduction
  • Option strategies for equity portfolios: standard long and short positions; risk management strategies with options and the underlying; money spreads; combinations of calls and puts
  • Interest rate option strategies using : interest rate calls with borrowing; interest rate puts with lending; an interest rate cap with a floating-rate loan; an interest rate floor with a floating-rate loan; an interest rate collar with a floating-rate loan
  • Option portfolio risk management strategies: delta hedging an option over time; gamma and the risk of delta; vega and volatility risk.


 CHAPTER                                                                                                                      PAGE NO

  1. Introduction to derivative markets and instruments……………………….6
  2. Forward markets and contracts…………………………………………………….13
  3. Futures markets and contracts………………………………………………..……39
  4. Risk management applications of forward and futures strategies……..77
  5. Swap markets and contracts……………………………………………………..….101
  6. Risk management application of swap strategies……………………………131
  7. Option markets and contracts…………………………………………….………..140
  8. Risk management applications of option strategies…………………………158






Derivatives markets and instruments

Derivatives – is a financial instrument that offers a return based on the returns of some other underlying assets i.e. its return is derived from another instrument hence the name. Derivative performance is based on the performance of an underlying instrument.

The underlying asset is often referred to the underlying and it trades in the market where buyers and sellers meet and decide on the price then the seller delivers the asset to the buyer and receives payment.

A Cash price or spot price refers to the price you immediate purchase of the asset.

A derivative has a defined and limited life which means a derivative contract initiates on a certain date and terminates on a later date. A derivative payoff is determined and /or made or the expiration date in most cases.

A derivative contract is an agreement between two parties in which each party does something for the other e.g an insurance contract where one party pays the other and in return receives coverage against potential losses.


Derivatives trade in the following markets;

Exchange Traded Market

They have standard terms and features and they have organized derivative trading facilities e.g. a future exchange as an option exchange.




A forward contract-is agreement between two parties in which one party the buyer agrees to buy from another party the seller an underlying asset or other derivatives at a future date at a price established at the start of the contract.

Therefore it is a commitment two parties to engage in a transaction at a later date with the price set in advance.

The buyer in the forward contract is often called the long and the seller is called the short.


  1. Forward contracts lock in the price and if the time the seller is supposed to deliver and the price goes lower than the set  price, he will still receive the  set price and benefit from having locked in the price. However if prices went up he will lose the chance of enjoying high prices in the marked since he will have to pay the set forward price.




Futures are standardized while forwards are customized.

Futures have exchange markets; forwards have no established distinct markets. Futures have guidelines performances or pa through cleaning house while

A future contract: – is an agreement between two parties to buy or sell an underlying or another at a future state at a price agrees on today.

Forwards Futures
Private & customized contracts Is a public transaction taking place in an organized futures exchange
All times an exposure two parties All the terms except for price is set future exchange hence they are standardized
There’s an exposure to credit The clearing house guarantee against future credit loss through a process called marking to market
Forwards are highly unregulated Futures are regulated the government
Can be created at any location Created in an organized facility called futures exchange





Hedging – taking a market position to protect against an undesirable outcome eg increase in interest rates. Companies do more than hedge, they may manage risk.

Manage risk-carefully consider scenarios and elect to adjust the risk they face to a level they feel is acceptable. This adjustment involves:

  • Reduction of risk
  • Altering the risk from current level to a level the company desires.


Many companies make plans to borrow based on their future cash needs at specific future dates. The rates they pay on these loans are important determinants of their future cash needs as reflected in their planned interest payments. Exposure to international rate risk is a major concern. Failure to manage interest rate risk can hinder planning process, as well as result in unexpected demands on cash necessitated unexpected higher international payments.

Managing international rate risk using FRA

  1. Single payment loan

A company anticipating to borrow money in the future enters into a long position in an FRA. The FRA has a fixed rate called the FRA. If underlying rate at expiration is above the FRA rate, the company as the holder of long position receives a lump sum of cash based on the difference between FRA rate and market rate at that time. This payment helps offset the higher the rate the company would be paying on its loan. If the rate in the market falls below FRA rate, however, the company will end up paying the counterparty, thereoffsetting the lower rate it




A swap is an agreement between two parties to exchange a series of future cash flows for market types of swaps, one party makes the payments that are determined a random outcome such as an interest rate, a currency rate, an equity return or a commodity price. These random payments are commonly referred to as variable or floating. The other party either makes variable or floating payments determined some other random factors or makes fixed payments. At least one type of swap involves both parties making fixed payments but the values of these payments vary due to random factors.

In swaps the floating/variable rate payer or the fixed rate payer are the preferred terminologies used to designate the parties  to a swap as opposed to the long and short parties  terminologies used in forwards, futures and options.

The party receiving a floating rate is said to be long while the one receiving the fixed rate is said to be short. In some cases however, both parties receive floating / variables hence the terminologies doesn’t apply in such cases.

Characteristics of swaps

  1. Most swaps involve multiple payments though there are times when swaps involve a single payment. Thus a swap is referred to as a series of payments. A swap with one payment is just a forward contract hence a swap is basically a series of forwards.
  2. When a swap is initiated neither party pays any amount to the other hence it has a zero value at the start of a contract with the exception of currency swaps where each party pays notional principal to the other the amount exchanged being equivalent though denominated in two different currencies.

Each date on which parties makes payments is called settlement date/payment date and the time between settlement date is called settlement period. On a given settlement date when payments are due, one party pays the other who in turn pays the first party and with the exception of currency swaps, all payments are done in the same or one currency. Consequently, parties agree to exchange only the net





Managing interest rate risk

The most common type of swap is a ‘‘plain vanilla’’ interest rate swap. In this swap a company agrees to pay cash flows equal to interest at a predetermined fixed rate on a notional principal for a predetermined number of years. In return, it receives interest at a floating rate on the same notional principal for the same period of time.

Interest Rate Risk Management

Interest rate swaps is the most widely used instrument to manage interest rate risk.

Swaps are not used to manage the risk of an anticipated loan, rather, they are designed to manage the risk of a series of Cash flows on loans already taken out or in the process of being taken out.

Swaps can also be used to manage the risk associated with managing a portfolio of bonds.

Converting a floating rate loan to a fixed rate loan and vice versa using interest rate swap


Using Swaps to adjust duration of fixed income portfolio

The duration of a swap is equivalent to the duration of a long position in a floating rate bond and a short position in a fixed rate bond.

Duration of a swap is the net of the durations of equivalent positions in fixed- and floating rate bond and a short position in a fixed rate bond. Negative duration means that a fixed rate payer is favored rising rates and falling market value.

Value of a bond portfolio is inversely related to interest rates.




NP = Notional principal




 An option; -is a financial derivative contract that provides a party the right to buy or sell an underlying at a fixed price a certain time in the future. The part buying the right is called the option buyer while the party granting the right is called option seller. There are 2 types of option. A call and a put option

Call option is an option granting the right to buy the underlying while a put option is an option of granting the right to sell the underlying.

With the exception of some advanced type of option, an option contract is either a call or a put but not both.

Basic characteristics of option

  1. The fixed price at which the option holder can buy or sell the underlying is called the exercise price/strike price /striking price/ strike price k
  2. The use of this right to buy or sell the underlying is referred to as exercise or exercising the option.
  3. An option has an expiration date giving rise to the notion of the options time to expiration. T -t
  4. When the expiration date arrives, an option that is not exercised simply expires. If the buyer is exercising a call he/she pays the exercise price and receives either the underlying on an equivalent cash settlement while on the opposite side the seller who receives the exercise price from the buyer delivers the underlying or pays equivalent cash settlement.
  5. If the buyer is exercising a put, he/she delivers a stock and receives the exercise price or an equivalent cash settlement .the seller on the other hand receives the underlying and must pay the exercise price or equivalent cash settlement. In cash settlement, the option holder exercising a call receives the difference between the market value and the exercise price from the seller in cash. If the option holder exercises a put, he receives the difference between the exercise price and the market value of the underlying in cash. There are 2 primary exercised styles associated with options.




Options have non-linear payoffs and permit their users to benefit from movements in the underlying in one direction and not to be harmed movements in the other direction in exchange for the premium paid up front.

Holders of the short position can have large losses due to options hence need to be compensated the premium and must skillfully manage the risk they assume.

Risk management through option strategies can be achieved through 3 major approaches:

  1. Equity investing risk management
  2. Interest rate risk management
  3. Option portfolio risk management


  1. Most of the options contracts are customized, over the counter options
  2. All options are European options – No consideration of terminating option early

(A)Option strategies for Equity portfolio

 Buy or sell short the underlying

Selling short involves borrowing the shares from a broker, selling them at the current price and then buying them back at a later date hence if you sell short the stock and it goes down, you make a profit and vice versa.


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