Financial Derivatives

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# Financial Derivatives - PowerPoint PPT Presentation

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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Presentation Transcript
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
Course Materials
• Textbook
• “Options, Futures, and Other Derivatives,” by John Hull
• Software
• How to contact me
• Email: spindt@tulane.edu
• Web: http//elvis.sob.tulane.edu
• Phone: (504) 865-5413
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 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
Introduction
• 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.
Introduction
• Derivatives markets are huge
• BIS estimate of OTC at 900 trillion (notional)
• Actual credit exposure is much smaller, but still very significant
• Possibly 15 to 20 trillion
• US GDP is roughly 14 trillion
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
• Most active forwards in foreign exchange

S(T)

S(T)

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.

F(0,T)

F(0,T)

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:
Futures
• 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
• 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
Futures
• 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
Options
• 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
Options

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

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

S(T)

X

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

S(T)

X

Options
• 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.
Options
• 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
• 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?
• 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.