Derivatives

1
Derivatives

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

2
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

3
Forward Markets

• Forward contract
• an agreement to transact involving the future
  exchange of a set amount of assets at a set price
• Forwards are traded over-the-counter
• Counterparty (or credit risk) is a major concern
• Forward markets are not very liquid

4
Futures Contracts

• Exchange traded products
• Regulated by the CFTC
• Types of Futures
• Commodity Futures
• Financial Futures
• stock index futures
• interest rate futures
• currency futures
• The value of a futures contract is derived from
  the value of the underlying instrument

5
Futures Contracts

• A firm legal agreement between a buyer and a
  seller.
• the buyer agrees to take delivery of an asset at
  a specified price at the end of a designated
  period of time.
• the seller agrees to make delivery of an asset at
  a specified price at the end of a designated
  period of time.

6
Futures Contracts

• Key Elements
• Futures Price
• Settlement Date or Delivery Date
• Underlying Asset
• Futures Positions
• Long futures
• Short futures

7
Liquidating a Futures Position

• Settlement Dates
• March, June, September, December
• Nearby futures contracts
• Most distant futures contracts
• Liquidating a Futures Position
• Take an offsetting position in the same contract
  prior to the settlement date
• Take delivery of the underlying asset on the date
  of settlement
• Open Interest

8
Role of Clearinghouse

• Functions of Clearinghouse
• guarantees that both parties to futures contracts
  satisfy their obligations
• simplifies the unwinding of futures positions
  prior to the settlement date

9
Margin Requirements

• Initial Margin
• minimum dollar amount per futures contract
• provides investor with substantial leverage
• Maintenance Margin
• minimum level to which an equity position may
  fall due to adverse price movements
• Variation Margin
• amount necessary to bring equity account back to
  initial margin level

10
Daily Settlement

• Futures contracts are marked-to-market daily
• a buyer (seller) realizes a profit if the futures
  price increases (decreases)
• a buyer (seller) realizes a loss if the futures
  price decreases (increases)
• Daily price limits restrict the maximum daily
  price moves

11
Market Structure

• Exchange Trading
• Pit
• Seat on the exchange
• Floor Traders
• Locals
• Floor or pit brokers
• Futures commissions merchant
• Electronic Trading Systems

12
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
• riskfree hedge
• riskfree rate of return

13
Hedge Positions

• Short Hedge
• protects against a decline in the cash price of a
  financial asset or portfolio
• sell hedge
• Long Hedge
• protects against an increase in the cash price of
  a financial asset or portfolio
• buy hedge

14
Risks of Futures

• Basis Risk
• Basis is the difference between the futures
  price and the spot market price
• The basis can change over time
• Liquidity Risk
• Must be able to meet margin calls
• Cross-hedging
• Asset underlying a futures contract may not
  exactly match the cash market risk exposure

15
Futures Versus Forward Contracts

• Type of Contract
• Trading Location
• Clearinghouse
• Settlement

• Delivery
• Collateral
• Credit Risk
• Basis and Liquidity Risk

16
The Role of Futures in Financial Markets

• Altering Risk Exposure of an Asset
• Price Discovery
• Arbitrage Process
• May Cause Increased Price Volatility of
  Underlying Asset

17
U.S. Financial Futures Markets

• Stock Index Futures Market
• Interest Rate Futures Market
• Treasury Bill Futures
• Eurodollar CD Futures
• Treasury Bond Futures
• Treasury Note Futures
• Agency Futures

18
Arbitrage Strategies

• Cash and carry trade
• borrowing cash to purchase a security and
  carrying that security to the futures settlement
  date
• Reverse cash and carry trade
• selling a security short and investing the
  proceeds received from the short sale

19
Pricing of Futures Contracts

• The theoretical or equilibrium futures prices is
  based on arbitrage arguments.
• The following information is needed
• The price of the asset in the cash market
• The cash yield earned on the asset until the
  settlement date
• The rate for borrowing and lending until the
  settlement date

20
A Theory of Futures Pricing

• The equilibrium futures price is the price that
  ensures the the profit from the arbitrage
  strategy is zero.
• Profit 0 F yP - (P rP)
• The theoretical futures price is
• F P P (r - y)

21
A Theory of Futures Pricing

• The theoretical futures price depends on
• The price of the underlying asset in the cash
  market.
• The cost of financing a position in the
  underlying asset.
• The cash yield on the underlying asset.

22
Theoretical Futures Price

• The effect of carry on the difference between the
  futures price and the cash price can be shows as
  follows

23
Principle of Convergence

• At the delivery date, the futures price must
  equal the cash price.
• As the delivery date approaches, the futures
  price converges to the cash price.
• The financing cost approaches zero
• The yield approaches zero
• The cost of carry approaches zero

24
Assumptions Underlying the Arbitrage Arguments

• No Interim cash flows
• No differences between lending and borrowing
  rates
• No transaction costs
• No limits on short selling
• Known deliverable asset and settlement date
• Deliverable is not a basket of securities
• No Difference in tax treatment of cash and
  futures transactions

25
Options Contracts

• The right, not the obligation, to either buy or
  sell a specified amount of a specific asset at a
  specified price within a specified period of time.

26
Options Terminology

• Option price or option premium
• Exercise price or strike price
• Expiration date or maturity date
• Call option or put option
• American option or European option
• Maximum profit or maximum loss
• Exchange-traded options or over-the-counter
  options

27
Risk/Return Characteristics of Call Options

• The purchase of a call is like taking a long
  position in the underlying asset with a fixed,
  maximum loss.
• Benefits the buyer if the price of the underlying
  asset rises.
• Benefits the seller if the price of the
  underlying asses falls or is unchanged.

28
Payoff Function for Call Options
29
Risk/Return Characteristics of Put Options

• The purchase of a put is like taking a short
  position in the underlying asset with a known
  maximum loss.
• Benefits the buyer if the price of the underlying
  asset falls.
• Benefits the seller if the price of the
  underlying asset rises or is unchanged.

30
Payoff Function for Put Options
31
Differences Between Options and Futures Contracts

• Both parties to a futures contract accept an
  obligation to transact, while only the options
  writer has such an obligation.
• The option buyer has a limited, known maximum
  loss.
• The risk/return profile of an option position is
  asymmetric, while that of a futures position is
  symmetric.

32
Economic Role of the Options Market

• Hedging With Futures
• Minimizes the risks of adverse price movements.
• Gives up the benefits of favorable price
  movements.
• Hedging With Options
• Limits price risk.
• May benefit from favorable price movements.
• May mold a risk/return relationship.

33
Pricing of Options

• The price of an option consists of two
  components the intrinsic value and the time
  premium.
• Intrinsic value
• the economic value of the option if exercised
  immediately, which is either greater than zero or
  zero
• Time premium
• amount by which the option price exceeds the
  intrinsic value

34
Call Option Value
35
Factors That Influence the Options Price

• Current price of the underlying asset
• Strike price
• Time to expiration of the option
• Expected price volatility of the underlying asset
  over the life of the option
• Short-term, riskfree interest rate over the life
  of the option
• Anticipated cash payments on the underlying asset
  over the life of the option

36
Option Pricing Models

• The theoretical options price is determined on
  the basis of arbitrage arguments.
• Option Pricing Models
• Black and Scholes Option Pricing Model
• Binomial Option Pricing Model

37
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

38
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

39
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

40
Fixed-Income Option Pricing Models

• Assumptions of Black-Scholes model are
  unreasonable for fixed-income securities
• Alternative option pricing models
• yield curve option pricing models
• arbitrage-free option pricing models

41
Put-Call Parity

• Relationship between the price of a call, and the
  price of a put
• On the same underlying asset
• With the same strike price
• With the same expiration date

42
Put-Call Parity

• Put-call parity for European options with cash
  distributions on underlying asset

where P Put option price C Call option
price X Strike price Dt Cash
distribution S Price of underlying asset rf
Riskfree rate
43
U.S. Options Markets

• Stock Options
• Stock Index Options
• Futures Options
• LEAPS

• Interest Rate Options
• Exotic Options

44
Interest Rate Swap

• An agreement whereby two parties agree to
  exchange periodic interest payments based on a
  notional principal amount.
• fixed rate payer
• floating rate payer
• reference rate
• Treasury bills, LIBOR, commercial paper, bankers
  acceptances, CDs, federal funds rate, prime rate

45
Risk/Return Characteristics of a Swap
46
Applications

• Asset/Liability Management
• Debt Issuance

47
Interest Rate Swap Market

• Initial motivation was borrower exploitations of
  perceived credit arbitrage opportunities.
• An efficient market for altering cash flow
  characteristics of assets or liabilities.
• Commercial banks and investment banking firms
  take positions in swaps.

48
Swaptions

• Grants the option buyer the right to enter into
  an interest rate swap at a future date.
• Types of Swaptions
• payer swaption
• receiver swaption

49
Interest Rate Caps and Floors

• An agreement between two parties in which one
  party, for an upfront premium, agrees to
  compensate the other if the reference rate is
  different from the strike rate.
• Interest Rate Cap
• Interest Rate Floor
• Strike Rate
• Combinations
• Interest Rate Collar
• Captions
• Flotions