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.comhttp://www.bloomberg.com Wall Street Jounral: http://online.wsj.comhttp://online.wsj.com Financial Times: http://www.ft.comhttp://www.ft.com Reuters: http://www.reuters.comhttp://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 K Price of Underlying at Maturity, ST Profit ST Long Position Short Position Gain Loss Price

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. Long Call on IBM Profit from buying an IBM European call option: option price = $5, strike price = $100, option life = 2 months 30 20 10 0 -5 708090100 110120130 Profit ($) Terminal stock price ($)

26. Short Call on IBM Profit from writing an IBM European call option: option price = $5, strike price = $100, option life = 2 months -30 -20 -10 0 5 708090100 110120130 Profit ($) Terminal stock price ($)

27. Long Put on Exxon Profit from buying an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths 30 20 10 0 -7 706050408090100 Profit ($) Terminal stock price ($)

28. Short Put on Exxon Profit from writing an Exxon European put option: option price = $7, strike price = $70, option life = 3 mths -30 -20 -10 7 0 70 605040 8090100 Profit ($) Terminal stock price ($)

29. Payoffs from Options What is the Option Position in Each Case? X = Strike price, S T = Price of asset at maturity Payoff STST STST X X STST STST X X

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 Fixed Rate Floating Rate Company A 9 % LIBOR + 0.4% Company B 12 % LIBOR + 1.2%

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