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Financial Derivatives

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Financial Derivatives. Introduction. Course Objective. Goal: To provide participants with a working knowledge of Derivatives markets Uses of derivatives Pricing of derivatives. Course Method. Pedagogy: Emphasis on practice Lectures Examples Problem set Take-home exam.

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course objective
Course Objective
  • Goal: To provide participants with a working knowledge of
    • Derivatives markets
    • Uses of derivatives
    • Pricing of derivatives
course method
Course Method
  • Pedagogy: Emphasis on practice
    • Lectures
    • Examples
    • Problem set
    • Take-home exam
course materials
Course Materials
  • Textbook
    • “Options, Futures, and Other Derivatives,” by John Hull
  • Software
    • Microsoft Excel spreadsheets
  • How to contact me
    • Email:
    • Web: http//
    • Phone: (504) 865-5413
course overview
Course Overview
  • Part I: Forwards, futures and swaps
    • Derivatives: Forwards,futures, and options
    • Interest rates
    • Pricing forwards and futures
    • Swaps
    • Problem set assignment (take home)
    • Option basics
course overview1
Course Overview
  • Part II: Options and derivative pricing
    • A binomial model
    • The Black-Scholes model
    • Option Greeks and volatility
    • Numerical methods
    • Interest rate derivatives
    • Credit derivatives(?)
    • Exam
  • A derivative is a financial contract whose value derives from some underlying asset.
    • i.e. derivatives are “side-bets”
  • The value of a derivative can be expressed as a function of some reference variable and other variables, such as time.
    • e.g. A call option on 100 shares of GE.
  • Derivatives allow risk to be separated from ownership of the underlying assets.
  • Derivatives markets are huge
    • BIS estimate of OTC at 900 trillion (notional)
    • About 100 trillion (notional) in exchange traded markets
  • Actual credit exposure is much smaller, but still very significant
    • Possibly 15 to 20 trillion
    • US GDP is roughly 14 trillion
forward contract
Forward Contract
  • Agreement to buy (long) or sell (short)
    • A certain asset (the reference asset)
    • On a certain future date (the maturity or expiration date)
    • For a certain price (the forward price)
      • The forward price is not the price of the forward contract!
  • Example: On April 6, 2009,
    • The spot price of £1 was $1.4742
    • The price of £1 for delivery 6 months forward was $1.4753
  • Forwards traded OTC
  • Most active forwards in foreign exchange
forward contract1



Forward Contract
  • Notation: F(t,T) is the forward price quoted at time t for delivery at T.
    • What is F(0,T)? What is F(T,T) = S(T)?
  • Payoff on a forward struck today (time 0) for delivery at time T is S(T) - F(0,T).
    • i.e. the spot price at time T minus the forward price at time 0.



forward contract2
Forward Contract
  • For a contract struck at time t for delivery at time T, the forward price on a zero-yield asset is related to the spot price of the asset and the market rate of interest:
  • Like a forward contact, in a futures contract
    • long agrees to purchase (short agrees to sell) the underlying asset
    • at a certain future time
    • for a certain price (the futures price)
  • Unlike a forward contract, futures contracts
    • Are exchange traded
      • Standardized, clearing house guaranteed
    • Are marked to market daily
      • At market close, contracts are revalued to zero: short compensates long if prices have risen; long compensates short if prices have fallen
    • Require margin
  • The natural gas contract traded on the NYMEX:
    • calls for delivery of 10,000 MMBtu at Henry Hub
    • is priced in $ per MMBtu quoted to $.001
      • one price “tick” is worth $10.00 per contract
    • requires initial margin of $6,750 and maintenance margin of $5,000
  • The S&P 500 index futures contract traded on the CME
    • is cash-settled
    • is priced in $250 per index point (index to 2 decimal places times 250); one tick is .10 index point = $25
    • initial margin = $28,125; maintenance margin = $22,500
  • Gives holder the right (but not the obligation) to
    • purchase (call option) or sell (put option) an underlying asset
    • by a certain date (expiry or expiration date)
    • for a certain price (exercise or strike price)
  • Most exchange traded options are American, though some index options are European
  • The underlying asset for the stock options traded on the CBOE is 100 shares of a given stock.
    • Option prices are quoted in $ per share of underlying

Example: Alcoa (AA) options prices on 4/7/09 when AA closed at $7.79

  • The payoff at expiration on a call option having an exercise price of X is max[S(T) - X, 0]:



  • The payoff at expiration on a put option having an exercise price of X is max[X - S(T), 0]:



  • The quantity max(j*[S(t)-X], 0), where j = 1 for calls and j = -1 for puts, is the intrinsic value of the option at time t.
  • An option is in-the-money, at-the-money, or out-of-the-money when j*[S(t)-X] is positive, zero, or negative.
    • In-the-money options have positive intrinsic value
    • At-the-money and out-of-the money options have zero intrinsic value
  • The excess of an option’s price over its intrinsic value is the option’s time value.
  • For example, on 4/7/09 when AA closed at $7.79
    • The $7.50 call expiring July 09 was in the money. Its price, $1.64, consisted of
      • Intrinsic value of $0.49 and
      • Time value of $1.15
    • The $7.50 put expiring in July 09 was out of the money. Its price, $1.33, consisted of
      • Intrinsic value of $0.00 and
      • Time value of $1.33
derivatives traders
Derivatives Traders
  • Hedgers use derivatives to shed the risk.
    • Hedgers tend to be naturally long or short the underlying asset and exposed to price risk
    • Price risk can be avoided (hedged) by taking an offsetting position in the derivatives market
  • Example: A US company expects to pay €1MM in 9 months time to settle an obligation. The company has a short position in Euros and is exposed to changes in the $/€ exchange rate. How to hedge?
  • Example: An investor owns 10,000 shares of Sun Microsystems (JAVA). The investor has a long position in JAVA shares. How can this investor hedge against a decline in JAVA share prices?
derivatives traders1
Derivatives Traders
  • Speculators use derivatives to take on risk.
  • Derivatives are leveraged positions in the underlying asset
    • Posting the initial margin ($6,750) and going long one NYMEX NatGas contract gives a speculator the price returns associated with $35,700 worth of NatGas at 4/6/09 prices.
      • On 4/7/09 the contract was up $0.11/MMBtu or $1,100 for one contract. On the initial margin, the return was 16%. On the unlevered cash position, the return was 3%.
    • To buy the price risk associated with 1000 shares of AA in the cash market would cost $7,790.00. Purchasing 10 call option contracts would be much cheaper.
derivatives traders2
Derivatives Traders
  • Arbitrageurs take advantage of small price discrepancies between “equivalent” portfolios
    • Actions drive prices in different markets into equilibrium
  • Example:
    • Spot price of Swiss Francs (CHF) was $0.8794 on 4/7/09
    • 6-month forward price was $0.8810
    • Suppose a 6-month European call was available with a strike price of $0.865 for a price of $0.015.
    • Consider buying the call and selling the forward.