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550.444 Introduction to Financial Derivatives

550.444 Introduction to Financial Derivatives. Introduction Weeks of September 4 and September 9, 2013. Principals. David R Audley, Ph.D.; Sr. Lecturer in AMS david.audley@jhu.edu Office: WH 212A; 410-516-7136 Office Hours: 4:30 – 5:30 Monday Teaching Assistant(s)

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550.444 Introduction to Financial Derivatives

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  1. 550.444Introduction to Financial Derivatives Introduction Weeks of September 4 and September 9, 2013

  2. Principals • David R Audley, Ph.D.; Sr. Lecturer in AMS • david.audley@jhu.edu • Office: WH 212A; 410-516-7136 • Office Hours: 4:30 – 5:30 Monday • Teaching Assistant(s) • Huang, Qiushun (qhuang13@jhu.edu) • Office Hours: Friday 4pm – 6pm • Ward, Brian (bward16@jhu.edu) • Office Hours: Monday & Wednesday 2pm – 3 pm

  3. Schedule • Lecture Encounters • Monday & Wednesday, 3:00 - 4:15pm, • Mergenthaler 111 • Section • Section 1: Friday 3:00 - 3:50pm, Hodson 211 • Section 2: Thursday 3:00 - 3:50pm, WH 304

  4. Protocol • Attendance • Lecture – Mandatory (default) for MSE Fin Math majors • Quizzes & Clickers • Section – Strongly Advised/Recommended • Assignments • Due as Scheduled (for full credit) • Must be handed in to avoid “incomplete” • Exceptions must be requested in advance

  5. Resources • Textbook • John C Hull: Options, Futures, and Other Derivatives, Prentice-Hall 2012 (8e) • Recommended: Student Solutions Manual • On Reserve in Library • Text Resources • http://www.rotman.utoronto.ca/~hull/ofod/Errata8e/index.html • http://www.rotman.utoronto.ca/~hull/TechnicalNotes/index.html

  6. Resources • Supplemental Material • As directed • AMS Website • http://jesse.ams.jhu.edu/~daudley/444 • Additional Subject Material • Class Resources & Lecture Slides • Industry & Street “Research” (Optional) • Consult at your leisure/risk • Interest can generate Special Topics sessions • Blackboard

  7. Measures of Performance • Mid Term Exam (~1/3 of grade) • Final Exam (~1/3 of grade) • Home work as assigned and designated and Quizzes (~1/3 of grade)

  8. Assignment • Thru week of Sept 9 (Next Week) • Read: Hull Chapter 1 (Introduction) • Read: Hull Chapter 2 (Futures Markets) • Problems (Due September 16) • Chapter 1: 17, 18, 22, 23; 34, 35 • Chapter 1 (7e): 17, 18, 22, 23; 30, 31 • Chapter 2: 15,16, 21, 22; 30 • Chapter 2 (7e): 15, 16, 21, 22; 27

  9. Assignment • For week of Sept 16 (in 2 Weeks) • Read: Hull Chapters 3 (Hedging with Futures) • Problems (Due September 23) • Chapter 3: 4, 7, 10, 17, 18, 20, 22; 26 • Chapter 3 (7e): 4, 7, 10, 17, 18, 20, 22; 26

  10. Assets and Cash • Stock, Bond, Commodity, … (Assets) • Risk vs. Return (Expected Return) • Cash (or Currency) • Held, on Deposit or Borrowed • Terminology • Assets – things we “own” (long) • Liabilities – what we “owe” (short)

  11. How Things Work • True Assets – A house, a company, oil, … • Ownership rights, contracts, & other legal instruments which represent the true asset • For us, many are indistinguishable from the asset; are the asset • Provide properties that can be quantified, assigned, subordinated and made contingent • Can be modeled

  12. Who Makes it Work • Investment Banks: Capital Intermediation • Companies into Stock • Borrowings into Bonds • Broker-Dealers & Markets (Exchanges) • Create everything else • Facilitate transfer/exchange (trading) • Investors • Under the Watchful Eyes of Regulators, Professional Associations and the Rule of Law

  13. Creation & Exchange of Securities and Instruments Secondary Issues Securities & Contracts Create Securities Make Markets Manage Invested Funds Collateral New Issue Securities Investment Banking Broker-Dealers & Exchanges Institutional Investors

  14. Two Fundamental Ideas in Modeling LOAN FROM STANDPOINT OF LENDER • Cash Flow • Cash flow diagram • Receive vs. Pay over Time • Payoff Cashflow • Payoff diagram • Gain vs. Loss against Price • Cashflows can depend on some other variable Repayment of Loan w/Interest at t0+T Receive t, time Pay Amount of Loan, t0 Gain S, Price K LONG STOCK AT PRICE K Loss

  15. Real World Situation - Cash • Japanese Bank; borrow US dollars (USD) to loan to its customers; term, 3 months • Go to Euromarket where it might be able to get an Interbank Loan T = 1/4 year Lt0 = 3 month interest rate in effect at t0 Receive (Borrow) USD t0 + T Borrow: USD Pay Back: USD x (1 + Lt0 x T) t0 Pay Back USD+Lt0x(.25)xUSD

  16. Real World Situation - Cash • What if Bank did not have credit line? • Could perform the same transaction as a Synthetic in the FX and domestic Yen mkt • Borrow Yen in local mkt for term T, at L(t0,Y) • Sell Yen and buy USD in spot FX mkt at e(t0,Y) • Finally, the bank buys Yen and sells USD in the forward FX market for delivery at t0+T

  17. Real World Situation - Cash • Cash Flows are Additive Borrow Y for T Buy USD sell Y at e(t0,Y) Y = e(t0,Y) x USD Buy Y forward for t0+T Y x (1 + L(t0,Y)xT) = f(t0,T;Y) x USD1 USD1 = USD x (1 + L(t0,$) x T) Y Yx(1+L(t0,Y)xT) + USD Y + Yx(1+L(t0,Y)xT) USDx(1+L(t0,$)xT) = USD USDx(1+L(t0,$)xT) t0 t0+T

  18. Real World Situation - Cash • What’s the difference; what’s interesting • International Banks have credit risk in the USD loan • For the synthetic, the International Bank exposure is in the forward contract only • No principal risk • Yen loan default is a domestic issue (central bank) • The synthetic can be used to price the derivative, ex- credit risk (what’s the derivative in this example?) • Each side could be the other’s hedge • Different markets involve many legal & regulatory differences

  19. Real World Situation - Tax • Situation: • In Sept ‘02, investor bought asset S, S0=$100 • EOM Nov, asset target reached at $150 (sell) • Sale yields gain of $50 (taxable) • Wash-Sale Rule prohibits: • Sell winner at $50 gain • Sell another asset, Z that’s down $50 to $50 to offset gain • Buy asset Z back next day as investor still likes it • Prohibited since trade is intentionally washing gain

  20. Real World Situation - Tax • Alternative Synthetic using Options • Call Option (Strike = S0) • Long has right to buy underlying at pre-specified price, S0 • Short has obligation to deliver underlying at that price • Expiration Payoff Chart + + S0 S S S0 - - For the LONG For the SHORT

  21. Real World Situation - Tax • Put Option (Struck at S0) • Long has right to sell underlying at pre-specified price, S0 • Short has obligation to accept delivery of underlying at S0 • Expiration Payoff Chart + + S0 S S S0 - - For the LONG For the SHORT

  22. Real World Situation - Tax • Consider the Synthetic (to offset 50 gain) • Buy another Z asset at 50 in Nov (11/26/02) • Sell an at-the-money call on Z • Strike, Z0 = 50 • Expiration >= 31 days later, but in 2002 (12/30/02) • Buy an at-the-money put on Z (same expiry) • At expiration, sell the Z asset or deliver into Call

  23. Real World Situation - Tax • Payoff Charts for the Synthetic + • Price at the expiration of the options, Ze • If Ze > 50: • Short Call looses money • as short has to deliver Z for 50 • Long Put is worthless • If Ze < 50: • Short Call is worthless • Long Put gains as the long can • sell Z for 50 • In either case the investor has • locked in the 50 price for the stock • bought at 100(FIFO) 50 Short Call Z - + 50 Long Put Z - + 50 Synthetic Short in Z Z -

  24. Real World Situation - Tax • The timing issue is important • According to US Tax law, wash sale rules apply if the investor acquires or sells a substantially identical property within a 31-day period • In the synthetic strategy, the second Z is purchased on 11/20; while the options expire on 12/30 when the first Z is sold (and the tax loss is “booked” – FIFO accounting)

  25. Real World Examples – Consequences & Implications • Strategies are Risk Free and Zero Cost (aside from commissions and fees) • We created a Synthetic (using Derivatives) and used it to provide a solution • Finally, and most important, these examples display the crucial role Legal & Regulatory frameworks can play in engineering a financial strategy (its the environment)

  26. Two Points of View • Manufacturer (Dealer) vs. User (Investor) • Dealer’s View: there are two prices • A price he will buy from you (low) • A price he will sell to you (high) • It’s how the dealer makes money • Dealer never has money; not like an investor • Must find funding for any purchase • Place the cash from any sale • Leverage

  27. Two Points of View • Dealers prefer to work with instruments that have zero value at initiation (x bid/ask) • Likely more liquid • No principal risk • Regulators, Professional Organizations, and the Law are more important for market professionals than investors • Dealers vs. Investors

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

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

  30. Derivatives Markets • Exchange traded • Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading • Contracts are standard; virtually no credit risk • 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

  31. Size of OTC and Exchange Markets Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market

  32. Ways Derivatives are Used • 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

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

  34. Terminology • The party that has agreed to buyhas what is termed a long position • The party that has agreed to sell has what is termed a short position

  35. Example • On May 24, 2010 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.4422 • This obligates the corporation to pay $1,442,200 for £1 million on November 24, 2010 • What are the possible outcomes?

  36. Profit Price of Underlying at Maturity, ST Profit (or Payoff) from aLong Forward Position K Payoff at T = ST – K

  37. Profit = Payoff at T = K - ST Price of Underlying at Maturity, ST Profit from a Short Forward Position K

  38. Foreign Exchange Quotes for GBP May 24, 2010

  39. Foreign Exchange Quotes for JPY Jan 22, 2007 (16:23 EST)

  40. 1. Gold: An Arbitrage Opportunity? Suppose that: • The spot price of gold is US$900 • The 1-year forward price of gold is US$1,020 • The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?

  41. 2. Gold: Another Arbitrage Opportunity? Suppose that: • The spot price of gold is US$900 • The 1-year forward price of gold is US$900 • The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?

  42. The Forward Price of Gold – The Principal of Cash and Carry • If the spot price of gold is S(t0)and the forward price for a contract deliverable in T years is F(t0,T), then • Can borrow money, buy gold, and sell the commodity forward - where there should be no arbitrage: F(t0,T) - S(t0) x(1+r)T = 0 where r is the 1-year money rate of interest to finance the gold carry trade. • In our examples, S = 900, T = 1, and r =0.05 so that F(t0,T)= 900(1+0.05) = 945 • The no arbitrage1 year forward price of gold is $945

  43. The Forward Price of Gold – The Principal of Cash and Carry • How does this come about? S(t0) receive Borrow S(t0) S(t0)x(1+r) pay t0 + Gold Buy Gold at S(t0) S(t0) + F(t0) Sell Gold Forward at F(t0) Gold = No Arbitrage condition says: F(t0) – S(t0)x(1+r) = 0 Gold Own Deliver Gold

  44. Gold Arbitrage? • The no arbitrage gold, 1-year forward condition is F(t0,T) - S(t0) x(1+r)T = 0 • If 1-year forward is $1020, then F(t0,T) - S(t0) x(1+r)T > 0 so our strategy is to borrow money, buy gold, sell it forward, deliver gold, and pay off loan for a riskless profit of $75 • If 1-year forward is $900, then F(t0,T) - S(t0) x(1+r)T < 0 and if I own gold, I can sell it, deposit proceeds, buy forward, pay with the proceeds of the deposit and collect a riskless profit of $45 over the 1-year period

  45. 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

  46. Futures Contracts • Forward contracts are similar to futures except that they trade in the over-the-counter market • Forward contracts are particularly popular on currencies and interest rates

  47. Exchanges Trading Futures • Chicago Board of Trade (CME) • Chicago Mercantile Exchange • LIFFE (London) • Eurex (Europe) • BM&F (Sao Paulo, Brazil) • TIFFE (Tokyo) • and many more (see list at end of book)

  48. Examples of Futures Contracts Agreement to: • Buy 100 oz. of gold @ US$1080/oz. in December (NYMEX) • Sell £62,500 @ 1.4410 US$/£ in March (CME) • Sell 1,000 bbl. of oil @ US$120/bbl. in April (NYMEX)

  49. 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 option is an option to sell a certain asset by a certain date for a certain price (the strike price)

  50. American vs European Options • An American style option can be exercised at any time during its life • A European style option can be exercised only at maturity

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