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金融工程导论

金融工程导论. 讲师： 何志刚，倪禾* Email: nihe@mail.zjgsu.edu.cn*. Reference & Online Resource. 金融工程 郑振龙 高等教育出版社 Options, Futures and other derivatives John C. Hull Prentice Hall Bloomberg: http://www.bloomberg.com Wall Street Jounral: http://online.wsj.com Financial Times: http://www.ft.com

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金融工程导论

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  1. 金融工程导论 讲师：何志刚，倪禾* Email:nihe@mail.zjgsu.edu.cn*

  2. Reference & Online Resource • 金融工程 郑振龙 高等教育出版社 • Options, Futures and other derivatives John C. Hull Prentice Hall • Bloomberg: http://www.bloomberg.com • Wall Street Jounral: http://online.wsj.com • Financial Times: http://www.ft.com • Reuters: http://www.reuters.com

  3. Introduction • What is finance • What is financial engineering • Why financial engineering

  4. Financial Engineering Emergence 1. Oil price: OPEC 2. Fixed – Floating foreign exchange rate: Bretton Wood system 3. Interests rate – inflation rate

  5. Financial Engineering Development • Advanced information technology Pricing, Fast process, Globel market • Efficiency of financial markets Gain profits and hedge risks

  6. Financial Engineering and Risk Management • Risk managemant is the key of FE Transfer risk i.e. Forward Split risk i.e. Portfolio

  7. The Nature of Derivatives • A derivative is an instrument whose value depends on the values of other more basic underlying variables

  8. Examples of Derivatives • Forward Contracts • Futures Contracts • Options • Swaps

  9. Derivatives Markets • Exchange Traded • standard products • trading floor or computer trading • virtually no credit risk • Over-the-Counter • non-standard products • telephone market • some credit risk

  10. Ways Derivatives are Used • To hedge risks • To reflect a view on the future direction of the market • To lock in 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

  11. Forward Contracts • A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) • A spot contract is an agreement to buy or sell immediately

  12. How a Forward Contract Works • The contract is an over-the-counter (OTC) agreement between 2 companies • The delivery price is usually chosen so that the initial value of the contract is zero • No money changes hands when contract is first negotiated and it is settled at maturity

  13. The Forward Price • The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) • The forward price may be different for contracts of different maturities

  14. 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

  15. Examples • On January 20, 1998 a trader enters into an agreement to buy £1 million in three months at an exchange rate of 1.6196 • This obligates the trader to pay $1,619,600 for £1 million on April 20, 1998 • What are the possible outcomes?

  16. Profit from a Forward Position Profit Long Position Price of Underlying at Maturity, ST Gain ST Price K Loss Short Position

  17. 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

  18. Arbitrage Opportunity (I) • 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?

  19. Arbitrage Opportunity (II) • 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?

  20. The Forward Price of Gold • If the spot price of gold is S , 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

  21. Arbitrage Opportunity (III) • Suppose that: • The spot price of oil is US$20 • The quoted 1-year futures price of oil is US$25 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  22. Arbitrage Opportunity (IV) • Suppose that: • The spot price of oil is US$20 • The quoted 1-year futures price of oil is US$21 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  23. Exchanges Trading Futures • Chicago Board of Trade • Chicago Mercantile Exchange • BM&F (Sao Paulo, Brazil) • LIFFE (London) • TIFFE (Tokyo)

  24. Options • 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)

  25. Profit ($) 30 20 10 Terminal stock price ($) 70 80 90 100 0 110 120 130 -5 Long Call on IBM • Profit from buying an IBM European call option: option price = $5, strike price = $100, option life = 2 months

  26. Profit ($) 110 120 130 5 0 70 80 90 100 Terminal stock price ($) -10 -20 -30 Short Call on IBM • Profit from writing an IBM European call option: option price = $5, strike price = $100, option life = 2 months

  27. Profit ($) 30 20 10 Terminal stock price ($) 0 40 50 60 70 80 90 100 -7 Long Put on Exxon • Profit from buying an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths

  28. Profit ($) Terminal stock price ($) 7 40 50 60 0 70 80 90 100 -10 -20 -30 Short Put on Exxon • Profit from writing an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths

  29. Payoff Payoff X X ST ST Payoff Payoff X X ST ST Payoffs from OptionsWhat is the Option Position in Each Case? X = Strike price, ST = Price of asset at maturity

  30. Swaps Definition: A derivative in which two counterparties agree to exchange one stream of cash flows against another stream. Objective: Hedge certain risks such as interest rate risk

  31. Fixed-to-floating interest rate swap

  32. Fixed-to-floating interest rate swap • Benefit from comparative advantage 9% + LIBOR + 1.2% = 10.2 % + LIBOR 12% + LIBOR + 0.4 % = 12.4% + LIBOR LIBOR: London inter bank offer rate

  33. Types of Traders • Hedgers • Speculators • Arbitrageurs • Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators

  34. Hedging Examples • A US company will pay £1 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract • An investor owns 500 IBM shares currently worth $102 per share. A two- month put with a strike price of $100 costs $4. The investor decides to hedge by buying put options

  35. Speculation Example • An investor with $7,800 to invest feels that Exxon’s stock price will increase over the next 3 months. The current stock price is $78 and the price of a 3-month call option with a strike of $80 is $3

  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?

  37. Exchanges Trading Options • Chicago Board Options Exchange • American Stock Exchange • Philadelphia Stock Exchange • Pacific Stock Exchange • European Options Exchange • Australian Options Market

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