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Financial Derivatives

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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Financial Derivatives

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  1. Financial Derivatives

  2. Introduction

  3. Course Objective • Goal: To provide participants with a working knowledge of • Derivatives markets • Uses of derivatives • Pricing of derivatives

  4. Course Method • Pedagogy: Emphasis on practice • Lectures • Examples • Problem set • Take-home exam

  5. Course Materials • Textbook • “Options, Futures, and Other Derivatives,” by John Hull • Software • Microsoft Excel spreadsheets • How to contact me • Email: spindt@tulane.edu • Web: http//elvis.sob.tulane.edu • Phone: (504) 865-5413

  6. 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

  7. 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

  8. 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.

  9. Introduction • 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

  10. 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

  11. 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)

  12. 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:

  13. 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 • 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

  14. 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

  15. 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

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

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

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

  19. 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.

  20. 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

  21. 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?

  22. 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.

  23. 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.

  24. Next: Futures

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