Derivatives

1
Derivatives

• A derivative security (derivative) is a financial
  security whose payoff is linked to another
  previously issued security

2
Examples of Derivatives

• Forward and futures contracts
• currency forwards and futures
• interest rate futures
• Options contracts
• call option
• put option
• Swaps
• currency swap
• interest rate swap

3
Uses of Derivatives

• Hedging Reducing risk
• Speculating Increasing risk
• Arbitrage Taking advantage of pricing
  differences between markets
• Leverage With derivatives you can control a
  large amount of the underlying asset with at
  relatively small initial investment.

4
Forwards and Futures

• Both are agreements to deliver (or take delivery
  of) a specified asset at a future date
• Prices of both are tied to the current price of
  the asset in the spot market
• Spot contract
• agreement to purchase (or sell) an asset
  immediately

5
Forward Markets

• Forward contract
• an agreement to transact involving the future
  exchange of a set amount of assets at a set price
• participants hedge the risk that future spot
  prices on an asset will move against them
• FIs are the major forward market participants
  and make a profit on the spread between the price
  at which they originate and sell forward contracts

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Risk of Forwards

• Market Risk
• Counter Party (Credit) Risk
• Operational Risk

7
Futures Markets

• Futures contract
• an agreement to transact involving the future
  exchange of a set amount of assets for a price
  that is settled daily - marked to market daily
• Initial margin
• a deposit required on futures trades to ensure
  terms of any futures contract will be met
• Maintenance margin
• the margin a futures trader must maintain once a
  futures position is taken.

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Futures Trading

• Occurs on organized exchanges such as CBT and CME
  or IMM
• Open-outcry auction - traders face each other and
  cry out their offer to buy or sell
• Floor broker - Exchange members who place trades
  from the pubic
• Professional traders - Exchange members who trade
  for their own account
• Position traders - take a position in the futures
  market based on their expectations of future
  prices

(continued)
9

• Day traders - exchange members who take a
  position within a day and liquidate it before
  days end
• Scalpers - exchange members who take positions
  for very short periods of time, sometimes only
  minutes, in an attempt to profit from active
  trading
• Long position - a purchase of a futures contract
• Short position - a sale of a futures contract
• Clearinghouse - the unit that oversees trading on
  the exchange and guarantees all trades made by
  the exchange traders
• Open interest - total number of futures, put
  options, or call option contracts outstanding at
  the beginning of the day

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Contract Time Lines
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General Principles of Hedging With Futures

• Major function of futures market
• transfer price risk from hedgers to speculators
• Perfect hedge
• any loss (profit) on one position is exactly
  offset by any profit (loss) on the other position

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Risks of Futures

• Market Risk
• Liquidity Risk
• Basis Risk
• Operational Risk

13
Options

• A contract that gives the holder the right, but
  not the obligation, to buy or sell an asset at a
  prespecified price within a specified period of
  time
• American option - can be exercised at any time
  before the expiration date
• European option - can only be exercised on the
  expiration date

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Definitions of a Call and a Put

• Call option
• an option that gives a purchaser the right, but
  not the obligation, to buy the underlying
  security from the writer of the option at a
  prespecified exercise price on a prespecified
  date
• Put option
• an option that gives a purchaser the right, but
  not the obligation, to sell the underlying
  security to the writer of the option at a
  prespecified price on a prespecified date

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Payoff Function for Call Options
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Payoff Function for Put Options
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Option Values

• Intrinsic value of an option
• the difference between an options exercise price
  and the underlying assets price
• Time value of an option
• the difference between an options price (or
  premium) and its intrinsic value

18
Intrinsic value vs. the Before Exercise Value of
a Call Option
19
Option Markets

• Options traded on the floor of CBOE by floor
  brokers, professional traders or a market maker
  for the particular option being traded
• Stock options - the underlying asset on a stock
  option contract is the stock of a publicly traded
  company, generally 100 shares
• Stock index options - the underlying asset on a
  stock index option is the value of a major stock
  market index (e.g., the DJIA or SP 500)
• Options give investors a way to hedge their
  existing stock portfolios

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Risks of Options Markets

• Market Risk
• Counter Party (Credit) Risk if over the counter
• Basis Risk
• Liquidity Risk
• Operational Risk

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Black-Scholes Model

• Formula for the value of a European call option
• C N(d1)S E(e-rT)N(d2)
• d1 ln(S/E) (r?2/2)T/(??T)
• d2 d1 - ??T

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Definitions

• C Call option price
• S Price of the underlying asset
• E Exercise price of the option
• r Risk-free rate of interest
• ? Standard deviation of return of asset
• T time to option expiration (fraction of year)
• e base of natural log or exponential function
• Ln(S/E) natural log of S/E
• N(d1) cumulative normal distribution evaluated
  at d1
• N(d2) cumulative normal distribution evaluated
  at d2

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Assumptions of the Model

• Markets are frictionless
• No transaction costs
• No taxes
• Information is simultaneously and freely
  available to all investors
• Variability in the underlying assets return is
  constant
• Probability distribution of underlying assets
  price is log normal
• Risk-free rate is constant and known over time
• No dividends paid on underlying asset
• No early exercise of option is allowed

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Factors That Affect Option Price

• Current price of underlying asset.
• Strike price.
• Time to expiration.
• Expected volatility of the price of the
  underlying asset.
• Short term risk free rate.

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Determinants of Option Prices
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Regulation of Futures and Options Markets

• The Commodity Futures Trading Commission (CFTC)
  is the primary regulator of futures markets
• protects the trading public by seeking to prevent
  misrepresentation and/or market manipulation
• approves new or proposed contracts to ensure they
  have economic purpose, conducts economic studies,
  enforces rules and provides regulatory
  surveillance
• The Securities and Exchange Commission (SEC) is
  the main regulator of stock options
• regulates trading of stock options and stock
  index options

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Swaps

• An agreement between two parties to exchange
  assets or a series of cash flows for a specific
  period of time at a specified price.
• Allow firms to better manage their interest rate,
  foreign exchange and credit risk
• Basic principle involves the transacting parties
  restructuring their asset or liability cash flows
  in a preferred direction

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Swaps Definitions

• Swap buyer - a party that makes the fixed-rate
  payments in an interest rate swap transaction
• Notional principal - principal amount involved in
  a swap
• Swap seller - a party that makes the
  floating-rate payments in an interest rate swap
  transaction

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Swaps Definitions

• Interest rate swap - an exchange of
  fixed-interest payments for floating-interest
  payments by two counterparties
• Currency swap - used to hedge against exchange
  rate risk from mismatched currencies on assets
  and liabilities

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Swap Transactions
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Fixed-Floating Rate Swap
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Risks of Swaps

• Market Risk
• Counter Party (Credit) Risk
• Basis Risk
• Liquidity Risk
• Operational Risk

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Caps, Floors, Collars and Swaptions

• Cap
• a call option on interest rates, often with
  multiple exercise dates
• Floor
• a put option on interest rates, often with
  multiple exercise dates
• Collar
• a position taken simultaneously in a cap and a
  floor
• Swaption
• An option to enter into a swap

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Hedging Interest Rate Risk

• FI owns 1,000,000 face value 7.125 coupon
  Treasury bonds that mature Feb 2023.
• Investment is funded with 6 month CDs
• Risk exposure
• If rates increase by 1 bonds decline in value by
  10.87.
• If rates decrease by 1 bonds increase in value
  by 12.81

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Futures Market Hedge

• Cash Market Risk exposure we lose if rates
  increase (prices decrease) and win if rates
  decrease (prices increase).
• Hedging position in futures market should move in
  the opposite direction of the cash market.

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T-Bond Futures

• One contract is for 100,000 face value
  hypothetical 6 coupon 20 year bond
• Delivery months
• March, June, September, December

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Futures Market Hedge

• Long futures position gains if prices increase
  and loses if prices decrease.
• Short futures position gains if prices decrease
  and loses of prices increase.
• Futures market hedge
• Short 10 T-Bond futures contracts.

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Risks of Futures Hedge

• Basis Risk
• Futures contract based on 6 coupon, cash
  position on 7.125 coupon.
• Futures contract based on exactly 20 year term,
  cash position not exactly 20 years.
• Liquidity risk
• If interest rates decrease (prices rise) will
  face margin calls.

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Option Market Hedge

• Cash Market Risk exposure we lose if rates
  increase (prices decrease) and win if rates
  decrease (prices increase).
• Hedging position in option market should protect
  us if rates increase (prices decrease), but allow
  us to gain if rates decrease (prices increase).

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T-bond Futures Options

• Options on T-bond futures contract.
• Each option is on one futures contract (100,000)
  face value.

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Hedging with Options

• Call option gains if prices increase and loses if
  prices decrease.
• Put option gains if prices decrease and loses of
  prices increase.
• Option market hedge
• Buy 10 put options on T-Bond futures.

42
Hedging with Options

• Cost to buy put options
• Current price of the March 03 futures contract
• 10820 10820/32
• February 03 Put Option Premiums
• Strike 108 premium 25/64
• Strike 109 premium 236/64

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Risks of Options Hedge

• Basis risk Same issues as futures
• Note Could try to find an OTC option to better
  match underlying risk, but then you have
  counter-party risk
• Option could expire worthless in which case you
  lose the premium.

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Hedging with Swaps

• Cash Market Risk exposure we are funding long
  term assets with short term liabilities.
• Hedging position with a swap should change the
  short term liability into a long term liability.

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Swap Contracts

• Pay floating 3-month LIBOR
• Pay fixed rate for 20 years - 5
• Note Current 3-month LIBOR is 1.43.

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Hedging with Swaps

• A pay-fixed receive floating swap would change
  the floating rate liability into a fixed rate
  liability.
• Note Since pay-fixed rate is 5 and LIBOR is
  1.43, this transaction would immediately
  increase borrowing costs

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Risks of Swap Hedge

• Counter-party risk
• Basis risk The floating rate in the swap is the
  3-month LIBOR rate, but the cash market cost is
  the 6-month CD rate.