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Derivative Securities- Learning Objectives

What is a derivative security?Important characteristics of a

derivative security;Markets for derivative securities;Terminology is used to describe

derivative transactions;How are prices for derivative

securities quoted?

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Derivative Securities- Learning Objectives

Similarities and differences between forward and futures contracts;

Put and Call option contracts;How are forward contracts, put

options, and call options related to one another?

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Forward and Futures Contracts - Learning Objectives

Hedge ratio and how it is calculated?What economic functions do the

forward and futures markets serve?Futures pricing;Agricultural futures and financial

futures;Stock Index futures;Currency futures

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Derivative InstrumentsValue is depends directly on, or is derived

from, the value of another security or commodity, called the underlying asset

Forward and Futures contracts are agreements between two parties - the buyer agrees to purchase an asset from the seller at a specific date at a price agreed to now

Options offer the buyer the right without obligation to buy or sell at a fixed price up to or on a specific date

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Why Do Derivatives Exist?Assets are traded in the cash or spot

marketIt is sometimes advantageous enter

into a transaction now with the exchange of asset and payment at a future time

Risk shiftingPrice formationInvestment cost reduction

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Derivative InstrumentsForward contracts are the right and full

obligation to conduct a transaction involving another security or commodity - the underlying asset - at a predetermined date (maturity date) and at a predetermined price (contract price) This is a trade agreement

Futures contracts are similar, but subject to a daily settling-up process

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Forward ContractsBuyer is long, seller is shortContracts are OTC, have

negotiable terms, and are not liquid

Subject to credit risk or default risk

No payments until expirationAgreement may be illiquid

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Futures Contracts

Standardized termsCentral market (futures exchange)More liquidityLess liquidity risk - initial marginSettlement price - daily “marking

to market”

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Options

The Language and Structure of Options Markets An option contract gives the

holder the right-but not the obligation-to conduct a transaction involving an underlying security or commodity at a predetermined future date and at a predetermined price

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Options

Buyer has the long position in the contract

Seller (writer) has the short position in the contract

Buyer and seller are counterparties in the transaction

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OptionsOption Contract Terms

The exercise price is the price the call buyer will pay to-or the put buyer will receive from-the option seller if the option is exercised

Option Valuation Basics Intrinsic value represents the value that the buyer

could extract from the option if he or she she exercised it immediately

The time premium component is simply the difference between the whole option premium and the intrinsic component

Option Trading Markets-options trade both in over-the-counter markets and on exchanges

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OptionsOption to buy is a call optionOption to sell is a put optionOption premium - paid for the optionExercise price or strike price - price

agreed for purchase or saleExpiration date

European options American options

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Options

At the money: stock price equals exercise price

In-the-money option has intrinsic value

Out-of-the-money option has no intrinsic value

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Investing With Derivative Securities

Call option requires up front payment allows but does not require future

settlement paymentForward contract

does not require front-end payment requires future settlement payment

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Options Pricing Relationships

Factor Call Option Put Option

Stock price + -Exercise price - +Time to expiration + +Interest rate + -Volatility of underlying + +stock price

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Profits to Buyer of Call Option

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)

Exercise Price = $70

Option Price = $6.125

Profit from Strategy

Stock Price at Expiration

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Profits to Seller of Call Option

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)

Exercise Price = $70

Option Price = $6.125

Stock Price at Expiration

Profit from Strategy

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Profits to Buyer of Put Option

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)

Exercise Price = $70

Option Price = $2.25

Profit from Strategy

Stock Price at Expiration

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Profits to Seller of Put Option

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)

Exercise Price = $70

Option Price = $2.25

Stock Price at Expiration

Profit from Strategy

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Creating Synthetic Securities Using Put-Call ParityRisk-free portfolio could be created

using three risky securities: stock, a put option, and a call option

With Treasury-bill as the fourth security, any one of the four may be replaced with combinations of the other three

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Put-Call-Forward ParityInstead of buying stock, take a long

position in a forward contract to buy stock

Supplement this transaction by purchasing a put option and selling a call option, each with the same exercise price and expiration date

This reduces the net initial investment compared to purchasing the stock in the spot market

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An Overview of Forward and Futures Trading

Forward contracts are negotiated directly between two parties in the OTC markets. Individually designed to meet specific needs Subject to default risk

Futures contracts are bought through brokers on an exchange No direct interaction between the two parties Exchange clearinghouse oversees delivery and

settles daily gains and losses Customers post initial margin account

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Hedging With Forwards and Futures

Create a position that will offset the price risk of another holding holding a short forward position against

the long position in the commodity is a short hedge

a long hedge supplements a short commodity holding with a long forward position

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Hedging With Forwards and FuturesRelationship between spot and forward

price movements basis is spot price minus the forward price for

a contract maturing at date T:BtT = St - Ft,T

forward price converges to the spot price as the contract expires

hedging exposure is correlation between future changes in the spot and forward contract prices and can be perfectly correlated with customized contracts

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Hedging With Forwards and Futures

Calculating the Optimal Hedge Ratio net profit from the position

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F

2

FS,COV

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Forward and Futures Contracts:Basic Valuation Concepts

Forward and futures contracts are not securities but, rather, trade agreements that enable both buyers and sellers of an underlying commodity or security to lock in the eventual price of their transaction

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Valuing Forwards and Futures Valuing forwards

tTTTtTt iFFQV 1,0,,

•Valuing futures

•contracts are marked to market daily

* = the possibility that forward and futures prices for the same commodity at the same point in time

might be different

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The Relationship Between Spot and Forward Prices

If you buy a commodity now for cash and store it until you deliver it, the price you want under a forward contract would have to cover: the cost of buying it now the cost of storing it until the contract

matures the cost of financing the initial purchase

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The Relationship Between Spot and Forward Prices

These are the cost of carry necessary to move the asset to the future delivery date TTTTT DiPCSSCSF ,0,0,00,00,0

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Financial Forwards and Futures: Applications and Strategies

Originally, forward and futures markets were organized largely around trading agricultural commodities

Recent developments in this area have involved the use of financial securities as the asset underlying the contract

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Financial Forwards and Futures: Applications and Strategies

Interest rate forwards and futures were among the first derivatives to specify a financial security as the underlying asset forward rate agreements interest rate swaps

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Financial Forwards and Futures: Applications and Strategies

Long-term interest rate futures Treasury bond and note contract mechanics

CBT $100,000 face valueT-bond >15 year maturityT-note 10 year - bond with 6.5 to 10 year

maturityT-note 5 year - bond with 4.25 - 5.25 yearsDelivery any day during month of delivery

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Financial Forwards and Futures: Applications and Strategies

Long-term interest rate futuresLast trading day 7 days prior to the end

of the monthQuoted in 32ndsYield quoted is for referenceTreasury bonds pay semiannual interestConversion factors for differences in

deliverable bonds

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Short-Term Interest Rate FuturesEurodollar and Treasury bill contract

mechanicsCreating a synthetic fixed-rate

funding with a Eurodollar stripCreating a TED spread

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Stock Index FuturesIntended to provide a hedge against

movements in an underlying financial asset

Hedging an individual stock with an index isolates the unsystematic portion of that security’s risk

Stock index arbitrage prominent in program trading

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Currency Forwards and Futures

Currency quotations Direct (American) quote in U.S. dollars Indirect (European) quote in non U.S.

currency Reciprocals of each other

Interest rate parity and covered interest arbitrage

365RateInterest U.S.1

365RateInterest Foreign 1

Spot ForwardT

T