chapter 9. derivatives futures options swaps futures options swaps

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Chapter 9. Derivatives Chapter 9. Derivatives Futures Options Swaps

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Chapter 9. DerivativesChapter 9. DerivativesChapter 9. DerivativesChapter 9. Derivatives

• Futures

• Options

• Swaps

• Futures

• Options

• Swaps

Derivatives: the basicsDerivatives: the basicsDerivatives: the basicsDerivatives: the basics

• Financial instrument

• Value depends on another assets i.e. value is derived from another

• Purpose: to transfer risk from one party to another

• Financial instrument

• Value depends on another assets i.e. value is derived from another

• Purpose: to transfer risk from one party to another

Derivative usesDerivative usesDerivative usesDerivative uses

• Used to Profit from expected price changes

of certain assets• Speculation

Manage the risk associated with price changes• Hedging

• Used to Profit from expected price changes

of certain assets• Speculation

Manage the risk associated with price changes• Hedging

Futures ContractsFutures ContractsFutures ContractsFutures Contracts

• Exchange of asset/commodity between two parties on a future date

• Price of asset/commodity set today

• Exchange of asset/commodity between two parties on a future date

• Price of asset/commodity set today

Two partiesTwo partiesTwo partiesTwo parties

• Buyer Long position Obligation to buy asset on settlement

date at agreed price• Seller

Short position Obliations to deliver asset on

settlement date and receive agreed price

• Buyer Long position Obligation to buy asset on settlement

date at agreed price• Seller

Short position Obliations to deliver asset on

settlement date and receive agreed price

• Standardized Sold on exchanges Settlement date Asset/commodity

• Exchanges Chicago: CME, CBOT New York: NYMEX, NYBOT (NYFE)

• Standardized Sold on exchanges Settlement date Asset/commodity

• Exchanges Chicago: CME, CBOT New York: NYMEX, NYBOT (NYFE)

what kinds of commodities, what kinds of commodities, assets?assets?what kinds of commodities, what kinds of commodities, assets?assets?

• agriculture: corn, wheat, livestock, cotton, tobacco

• mining: metals, oil, natural gas

• Tbills, Tbonds (interest rate)

• Stock indexes (cash settlement)

• Foreign currencies (exchange rate)

• agriculture: corn, wheat, livestock, cotton, tobacco

• mining: metals, oil, natural gas

• Tbills, Tbonds (interest rate)

• Stock indexes (cash settlement)

• Foreign currencies (exchange rate)

• As price of underlying rises long position gains short position loses

• As price of underlying falls long position loses short position gains

• As price of underlying rises long position gains short position loses

• As price of underlying falls long position loses short position gains

Example 1: commodityExample 1: commodityExample 1: commodityExample 1: commodity

• Baker with a military contract locked in a price for bread Risk: fluctuating price of wheat• higher costs cannot be passed on to

bread buyers

• Baker with a military contract locked in a price for bread Risk: fluctuating price of wheat• higher costs cannot be passed on to

bread buyers

• solution? hedge with futures contract wheat futures contract, long

position locks in wheat price for buyer As wheat price rises, long position

gains to offset baker’s costs

• solution? hedge with futures contract wheat futures contract, long

position locks in wheat price for buyer As wheat price rises, long position

gains to offset baker’s costs

• but as wheat prices fall long position loses value to offset

lower costs for the baker

• but as wheat prices fall long position loses value to offset

lower costs for the baker

• who is the seller of the wheat futures contract? wheat farmers, grain elevator

companies speculators who believe wheat

prices will fall

• who is the seller of the wheat futures contract? wheat farmers, grain elevator

companies speculators who believe wheat

prices will fall

Example 2: financial assetExample 2: financial assetExample 2: financial assetExample 2: financial asset

• Savings and Loan borrow short term w/ deposits lend mostly long term fixed rate

• risk: short term interest rates rise higher costs without higher income

to match

• solution: short position in Tbill futures

• Savings and Loan borrow short term w/ deposits lend mostly long term fixed rate

• risk: short term interest rates rise higher costs without higher income

to match

• solution: short position in Tbill futures

• As interest rates rise, Tbill price falls, short position gains to offset

banking losses

• As interest rates rise, Tbill price falls, short position gains to offset

banking losses

Futures tradingFutures tradingFutures tradingFutures trading

• the exchanges form a clearing corporation that guarantees each party against default it is the counterparty to each

transaction

• the exchanges form a clearing corporation that guarantees each party against default it is the counterparty to each

transaction

• how does the exchange control its default risk? margin accounts• initial margin (10% or less of

contract value)

• daily gains/losses are marked to market

•margin calls if account gets too low

• how does the exchange control its default risk? margin accounts• initial margin (10% or less of

contract value)

• daily gains/losses are marked to market

•margin calls if account gets too low

example: Tbond contract (CBOT)example: Tbond contract (CBOT)example: Tbond contract (CBOT)example: Tbond contract (CBOT)

• $100,000 face value, 6% coupon

• initial margin = $2700

• Tbond price falls by 16/32 per $100 $500 price decrease

• buyer account falls to $2200

• seller account rises to $3200

• $100,000 face value, 6% coupon

• initial margin = $2700

• Tbond price falls by 16/32 per $100 $500 price decrease

• buyer account falls to $2200

• seller account rises to $3200

Options contractsOptions contractsOptions contractsOptions contracts

• 2 counterparties buyer/option holder seller/option writer

• buyer has rights, seller has obligations

• 2 counterparties buyer/option holder seller/option writer

• buyer has rights, seller has obligations

call optioncall optioncall optioncall option

• buyer has right to buy underlying at the strike price on/before a specific date writer has obligation to sell, if the

buyer chooses to buy

• buyer has right to buy underlying at the strike price on/before a specific date writer has obligation to sell, if the

buyer chooses to buy

put optionput optionput optionput option

• buyer has right to sell underlying at the strike price on/before a specific date writer has obligation to buy, if the

option holder chooses to sell

• buyer has right to sell underlying at the strike price on/before a specific date writer has obligation to buy, if the

option holder chooses to sell

• note: writer receives option price from buyer in exchange for taking on the obligation

• note: writer receives option price from buyer in exchange for taking on the obligation

• American options exercised any time until expiration

• European options exercised only on the day of

expiration

• American options exercised any time until expiration

• European options exercised only on the day of

expiration

• P = price of underlying

• X = strike price

• Qc = call option price

• Qp = put option price

• P = price of underlying

• X = strike price

• Qc = call option price

• Qp = put option price

when will options be exercised?when will options be exercised?when will options be exercised?when will options be exercised?

• call option – right to buy if P > X, then this option is in the

money if P < X, then this option is out of

the money

• call option – right to buy if P > X, then this option is in the

money if P < X, then this option is out of

the money

• put option – right to sell if P > X, then this option is out of

the money if P < X, then this option is in the

money

• put option – right to sell if P > X, then this option is out of

the money if P < X, then this option is in the

money

ExampleExampleExampleExample

• Google stock expiring 10/19/2007 P = $635/share call option• X = $500• Qc = $138.20• This option in the money

• Google stock expiring 10/19/2007 P = $635/share call option• X = $500• Qc = $138.20• This option in the money

put option• X = $500• Qp = $.10• This option is out of the money

put option• X = $500• Qp = $.10• This option is out of the money

Option tradingOption tradingOption tradingOption trading

• types of assets commodities bonds stocks and stock indexes

• exchange-traded & standardized

• Options Clearing Corporation

• types of assets commodities bonds stocks and stock indexes

• exchange-traded & standardized

• Options Clearing Corporation

• CBOE 10% options exercised 60% “traded out” (cash settlement) 30% expire worthless

• CBOE 10% options exercised 60% “traded out” (cash settlement) 30% expire worthless

Uses of optionsUses of optionsUses of optionsUses of options

• Who buys a call option? protection from a price increase of

the underlying (hedger)• option acts as insurance

betting on a price increase of the underlying (speculator)

• Who buys a call option? protection from a price increase of

the underlying (hedger)• option acts as insurance

betting on a price increase of the underlying (speculator)

• Who writes a call option? betting that the underlying price

will not rise broker always selling the

underlying and willing to be paid for the risk of the price rising

• Who writes a call option? betting that the underlying price

will not rise broker always selling the

underlying and willing to be paid for the risk of the price rising

• who buys a put option? protects from price decrease of

underlying in the future• hopes to sell underlying in the future

betting the price of underlying will fall

• who buys a put option? protects from price decrease of

underlying in the future• hopes to sell underlying in the future

betting the price of underlying will fall

• Who writes a put option? betting that the underlying price

will not fall broker always buying the

underlying and willing to be paid for the risk of the price falling

• Who writes a put option? betting that the underlying price

will not fall broker always buying the

underlying and willing to be paid for the risk of the price falling

The value of optionsThe value of optionsThe value of optionsThe value of options

• option price has two parts intrinsic value• value of option if exercised/expire now• depends on if in/out of the money• for a call: max (P-X, 0)• for a put: max (X-P, 0)

option premium• fee paid for having the option

• option price has two parts intrinsic value• value of option if exercised/expire now• depends on if in/out of the money• for a call: max (P-X, 0)• for a put: max (X-P, 0)

option premium• fee paid for having the option

exampleexampleexampleexample

• Google, P =$635, X = $500

• Qc = $138.20, Qp = $.10

• call option intrinsic value = 635- 500 = 135 premium = 138.20 – 135 = 3.20

• Google, P =$635, X = $500

• Qc = $138.20, Qp = $.10

• call option intrinsic value = 635- 500 = 135 premium = 138.20 – 135 = 3.20

• put option intrinsic value = 0• option is out of the money

premium = $.10

• put option intrinsic value = 0• option is out of the money

premium = $.10

What affects the price of an What affects the price of an option?option?What affects the price of an What affects the price of an option?option?

• P, price of underlying as P rises• affects the intrinsic value• call option price rises • put option price falls

• P, price of underlying as P rises• affects the intrinsic value• call option price rises • put option price falls

• X, the strike price as X rises• affects the intrinsic value• call option price falls• put option price rises

• X, the strike price as X rises• affects the intrinsic value• call option price falls• put option price rises

• time to expiration longer the time, higher the option

price of put or call options• higher premium• greater uncertainty about option being

in or out of the money

• time to expiration longer the time, higher the option

price of put or call options• higher premium• greater uncertainty about option being

in or out of the money

• volatility of P greater the volatility, the greater

the option price for both puts and calls• higher premium• greater uncertainty about option being

in or out of the money

• volatility of P greater the volatility, the greater

the option price for both puts and calls• higher premium• greater uncertainty about option being

in or out of the money

SwapsSwapsSwapsSwaps

• Interest rate swaps plain vanilla swap

• not standardized or exchange-traded more default risk less liquid BUT customized to specific needs

• Interest rate swaps plain vanilla swap

• not standardized or exchange-traded more default risk less liquid BUT customized to specific needs

How does a swap workHow does a swap workHow does a swap workHow does a swap work

• 2 counterparties

• exchange interest rate payments every 6 months over so many years

• one party pays a fixed rate

• one party pays a floating rate tied to 6 mo. Tbill

• 2 counterparties

• exchange interest rate payments every 6 months over so many years

• one party pays a fixed rate

• one party pays a floating rate tied to 6 mo. Tbill

• size of interest payments? based on notional principle• the principle never changes hands, just

determines the size of the interest payments

• size of interest payments? based on notional principle• the principle never changes hands, just

determines the size of the interest payments

• Bank pays 7% to dealer, receiving 6 mo. Tbill +3% from dealer• Dealer receives 7% from bank, pays 6 mo. Tbill +3% to bank

• notional principle = $100 million

• suppose 6 mo. Tbill is 4.2%

• Bank pays 7%, gets 7.2% bank net gain = $200,000 dealer net loss = $200,000

• notional principle = $100 million

• suppose 6 mo. Tbill is 4.2%

• Bank pays 7%, gets 7.2% bank net gain = $200,000 dealer net loss = $200,000

why swap?why swap?why swap?why swap?

• banks pay floating rates to depositors, but received fixed rates on loans the swap offsets their interest rate

risk

• dealer willing to assume the risk for profit potential

• banks pay floating rates to depositors, but received fixed rates on loans the swap offsets their interest rate

risk

• dealer willing to assume the risk for profit potential

U.S. Treasury debt managersU.S. Treasury debt managersU.S. Treasury debt managersU.S. Treasury debt managers

• long term bonds have strong demand

• but short term bonds match up to short term fluctuations in revenue

• solution? a swap

• long term bonds have strong demand

• but short term bonds match up to short term fluctuations in revenue

• solution? a swap

• government issues long term debt

• enters swap as floating rate payer recession• as rates fall swap results in net gain• but tax revenues fall as well

expansion• as rates rise swap results in net loss• but tax revenues rise as well

• government issues long term debt

• enters swap as floating rate payer recession• as rates fall swap results in net gain• but tax revenues fall as well

expansion• as rates rise swap results in net loss• but tax revenues rise as well