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Financial Derivative

Financial Derivative. Reference ： Options, Futures and Other Derivatives, John Hull, 5th and 3rd Edition. 2. 金融工程－－衍生品与风险管理， K. Cuthbertso, D. Nitzsche, 张陶伟 等译。. Schedule:. Lec 1: Introduction; Chapters 1 Lec 2: Outlines of Futures (market, hedging,

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Financial Derivative

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  1. Financial Derivative • Reference： • Options, Futures and Other Derivatives, John Hull, 5th and 3rd Edition. • 2. 金融工程－－衍生品与风险管理，K. • Cuthbertso, D. Nitzsche, 张陶伟 等译。 北航金融系李平

  2. Schedule: • Lec 1: Introduction; Chapters 1 • Lec 2: Outlines of Futures (market, hedging, valuation) , Chapter 2-4 • Lec 3: Interest Rate Futures, • Lec 4: Swaps, Chapter 6 (contingent) • Lec 5: Outline of Options (market 7, property 8, binomial 10) • Lec 6: Wiener processes and Ito's lemma; Chapter 11 • Lec 7: The Black-Scholes differential equation; Chapter 12 • Lec 8: Options on Stock Indices, Currencies, and Futures, Chapters 13 北航金融系李平

  3. Schedule (cont.): • Lec 9: The Greeks, Chapters 14 • Lec 10: Numerical procedures: Binomial & trinomial trees, Monte Carlo simulation; finite difference methods (Chapter 17) (contingent?) • Lec 11: Exotic options; Chapters 19 • Lec 12: Interest rate derivatives; Chapters 22 • Lec 13: Credit risk and credit derivatives; Chapters 27 • Lec 14: Real options, Chapter 28 • Lec 15: Insurance, weather and energy derivatives, Chapter 29; • Lec 16: Derivatives mishaps and what we can learn from them; Chapter 30 北航金融系李平

  4. Lecture 1(Chapter 1) Introduction 北航金融系李平

  5. Outline • 1. Derivatives • 2. Forward Contracts • 3. Futures Contracts • 4. Options • 5. Types of Traders • 6. Other Derivatives 北航金融系李平

  6. 1. Derivatives The Nature of Derivatives A derivative is an instrument whose value depends on the values of other more basic underlying variables. 北航金融系李平

  7. Examples of Derivatives • Forward Contracts • Futures Contracts • Swaps • Options 北航金融系李平

  8. Derivatives Markets • Exchange-traded markets • CBOT (Chicago Board of Trade), 1848, grain • CME (Chicago Mercantile Exchange), 1919, futures • CBOE (Chicago Board Options Exchange), 1973, options • Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading • Contracts are standard there is virtually no credit risk 北航金融系李平

  9. Over-the-counter (OTC) • A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers • Contracts can be non-standard and there is some small amount of credit risk 北航金融系李平

  10. Ways Derivatives areUsed • To hedge risks • To speculate (take a view on the future direction of the market) • To lock in an arbitrage profit • To change the nature of a liability • To change the nature of an investment without incurring the costs of selling one portfolio and buying another 北航金融系李平

  11. 2. Forward Contracts • A forward contract is an agreement to buy or sell an asset at a certain future time for a certain price (the delivery price) • It can be contrasted with a spot contract which is an agreement to buy or sell immediately • It is traded in the OTC market • Forward contracts on foreign exchange are very popular 北航金融系李平

  12. Foreign Exchange Quotes for GBP on Aug 16, 2001 北航金融系李平

  13. Terminology • The party that has agreed to buy has what is termed a long position • The party that has agreed to sell has what is termed a short position 北航金融系李平

  14. Example • On August 16, 2001 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.4359 • This obligates the corporation to pay $1,435,900 for £1 million on February 16, 2002 • What are the possible outcomes? 北航金融系李平

  15. Payoff Price of Underlying at Maturity, ST Payoff from a Long Forward Position K 北航金融系李平

  16. Payoff Price of Underlying at Maturity, ST Payoff from a Short Forward Position K 北航金融系李平

  17. Forward Price • The forward price for a contract is the price agreed today for the delivery of the asset at the maturity date. • When move through time the delivery price for the forward contract does not change, but the forward price is likely to do so. 北航金融系李平

  18. 1) Gold: An Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$340 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity? (We ignore storage costs and gold lease rate)? 北航金融系李平

  19. 2) Gold: Another Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$300 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity? 北航金融系李平

  20. The Forward Price of Gold If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S(1+r)T where r is the 1-year (domestic currency) risk-free rate of interest. In our examples, S = 300, T = 1, and r =0.05 so that F= 300(1+0.05) = 315 北航金融系李平

  21. 3. Futures Contracts • Agreement to buy or sell an asset for a certain price at a certain time • Similar to forward contract • Whereas a forward contract is traded OTC, a futures contract is traded on an exchange 北航金融系李平

  22. Examples of Futures Contracts • Agreement to: • buy 100 oz. of gold @ US$300/oz. in December (COMEX) • sell £62,500 @ 1.5000 US$/£ in March (CME) • sell 1,000 brl. of oil @ US$50/brl. in April (NYMEX) 北航金融系李平

  23. A call option is an option to buy a certain asset by a certain date for a certain price (the strike price) A put is an option to sell a certain asset by a certain date for a certain price (the strike price) 4. Options 北航金融系李平

  24. Terminology • Strike price (Exercise price) • Expiration date (maturity) • American/European option 北航金融系李平

  25. Options Exchanges • Chicago Board Options Exchange • American Stock Exchange • Philadelphia Stock Exchange • Pacific Stock Exchange • European Options Exchange • Australian Options Market • and many more (see list at end of book) 北航金融系李平

  26. Profit ($) 30 20 10 Terminal stock price ($) 30 40 50 60 0 70 80 90 -5 Long Call on Microsoft Profit from buying a European call option on Microsoft: option price = $5, strike price = $60 北航金融系李平

  27. Profit ($) 70 80 90 5 0 30 40 50 60 Terminal stock price ($) -10 -20 -30 Short Call on Microsoft Profit from writing a European call option on Microsoft: option price = $5, strike price = $60 北航金融系李平

  28. Profit ($) 30 20 10 Terminal stock price ($) 0 60 70 80 90 100 110 120 -7 Long Put on IBM Profit from buying a European put option on IBM: option price = $7, strike price = $90 北航金融系李平

  29. Profit ($) Terminal stock price ($) 7 60 70 80 0 90 100 110 120 -10 -20 -30 Short Put on IBM Profit from writing a European put option on IBM: option price = $7, strike price = $90 北航金融系李平

  30. Payoffs from Options K = Strike price, ST = Price of asset at maturity • Payoff from a long position in the European call: Max(ST-K,0) • Payoff from a short position in the European call: -Max(ST-K,0) • Payoff from a long position in the European putl: Max(K-ST,0) • Payoff from a long position in the European call: -Max(K-ST,0) 北航金融系李平

  31. Payoff Payoff K K ST ST Payoff Payoff K K ST ST Payoffs from Options 北航金融系李平

  32. 5. Types of Derivative Traders • Hedgers: use derivatives to reduce the risk that they face from potential future movements in a market variable • Speculators: use derivatives to bet on the future direction of a market variable • Arbitrageurs: lock in a riskless profit by simultaneously entering into two or more transactions 北航金融系李平

  33. Hedging Examples (1) • A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract • The price is locked, but the outcome may be worse 北航金融系李平

  34. Hedging Examples (2) • An investor owns 1,000 Microsoft shares currently worth $73 per share. • The investor decides to hedge the risk of decline by buying 10 two-month put with a strike price of $65 which costs $2.50. • The difference between the use of forward and options for hedging: • Forward: fix the price • Option: provide insurance 北航金融系李平

  35. Speculation Example • An investor with $4,000 to invest feels that Cisco’s stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of 25 is $1 • Two possible alternative strategies: buy calls and shares. • The use of futures and options for speculation: • Both obtain leverage • The potential loss and gain are different 北航金融系李平

  36. Arbitrage Example • A stock price is quoted as £100 in London and $172 in New York • The current exchange rate is 1.7500 • What is the arbitrage opportunity? • Arbitrage opportunities can’t last for long. 北航金融系李平

  37. 6. Other Derivatives • Plain vanilla/ standard derivatives • Exotics • Credit derivatives: creditworthiness of a company • Weather derivatives: average temperature • Insurance derivatives: dollar value of insurance claim • Electricity derivatives: spot price of electricity 北航金融系李平

  38. Lecture 2(Chapters 2,3,4) Futures 北航金融系李平

  39. 1. Futures Market • CBOT, CME • Available on a wide range of underlying assets • Specifications need to be defined: • What can be delivered, • Where it can be delivered, • When it can be delivered • Settled daily 北航金融系李平

  40. Delivery • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity • If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. • When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. • A few contracts (for example, those on stock indices and Eurodollars) are settled in cash 北航金融系李平

  41. Price and Position Limits • Many futures exchanges set limits on daily price changes and holdings. • Limits are set to prevent excessive volatility and market manipulation. • Limits are often removed in the last month of the contract. 北航金融系李平

  42. Convergence of Futures to Spot Futures Price Spot Price Futures Price Spot Price Time Time (a) (b) 北航金融系李平

  43. Margin Requirement • Initial Margin - funds deposited to provide capital to absorb losses, generally 5%-15%. • Maintenance Margin - an established value below which a trader’s margin may not fall. • Marking to market • When the maintenance margin is reached, the trader will receive a margin call from her broker to add variation margin to reach the level of initial margin. 北航金融系李平

  44. Margin Requirement (cont.) • 清算所(clearing house): track all the transactions to calculate the positions • 经纪人也需在清算所存入保证金(clearing margin) 。但数额小于等于客户交给经纪人的保证金 • 变动保证金必须以现金支付，初识保证金中的一部分可以以生息债券存入。 • 1990年7月某经纪公司对国际货币市场合约初始保证金和维持保证金的要求如下表。 北航金融系李平

  45. Margin Requirement (cont.) 合约 初始保证金 维持保证金 英镑 $2 800 $2 100 马克 $1 800 $1 400 瑞士法郎 $2 700 $2 000 日元 $2 700 $2 000 加拿大元 $1 000 $800 澳大利亚元 $2 000 $1 500 北航金融系李平

  46. Margin Calculation • An investor takes a long position in 2 December gold futures contracts on June 4 • contract size is 100 oz. • futures price is US$400 • initial margin requirement is US$2,000/contract (US$4,000 in total, 5%) • maintenance margin is US$1,500/contract (US$3,000 in total) 北航金融系李平

  47. Margin Calculation (cont.) Daily Cumulative Margin Futures Gain Gain Account Margin Price (Loss) (Loss) Balance Call Day (US$) (US$) (US$) (US$) (US$) 400.00 4,000 5-Jun 397.00 (600) (600) 3,400 0 . . . . . . . . . . . . . . . . . . 13-Jun 393.30 (420) (1,340) 2,660 1,340 4,000 + = . . . . . . . . . . . . . . . . . 3,000 < 19-Jun 387.00 (1,140) (2,600) 2,740 1,260 4,000 + = . . . . . . . . . . . . . . . . . . 26-Jun 392.30 260 (1,540) 5,060 0 北航金融系李平

  48. Example An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a margin call? Under what circumstances could $2,000 be withdrawn from the margin account? Falls by 10 cents and rises by 6.67 cents 北航金融系李平

  49. Newspaper quotes • Settlement price: the price just before the final bell each day • used for the daily settlement process • Open interest: the total number of contracts outstanding • equal to number of long positions or number of short positions • One trading older • Volume of trading: the number of trades in 1 day 北航金融系李平

  50. Patterns of Futures Prices • Normal market: price increase as the time to maturity increase, wheat in CBT • Inverted market: Sugar-World • Mixed pattern: crude oil • Normal backwardation (现货溢价): futures price below the expected spot price • Contango (期货溢价): above 北航金融系李平

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