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Derivatives Introduction

Derivatives Introduction . Professor André Farber Solvay Business School Université Libre de Bruxelles. 1.Introduction. Outline of this session Course outline Derivatives Forward contracts Options contracts The derivatives markets Futures contracts. Reference:

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Derivatives Introduction

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  1. DerivativesIntroduction Professor André Farber Solvay Business School Université Libre de Bruxelles

  2. 1.Introduction • Outline of this session • Course outline • Derivatives • Forward contracts • Options contracts • The derivatives markets • Futures contracts Derivatives 01 Introduction

  3. Reference: John HULL Options, Futures and Other Derivatives, Sixth edition, Pearson Prentice Hall 2006 or John HULL Options, Futures and Other Derivatives, Fifth edition, Prentice Hall 2003 • Copies of my slides will be available on my website: www.ulb.ac.be/cours/solvay/farber • Grades: • Cases: 30% • Final exam: 70% Derivatives 01 Introduction

  4. Course outline Derivatives 01 Introduction

  5. Derivatives • A derivative is an instrument whose value depends on the value of other more basic underlying variables • 2 main families: • Forward, Futures, Swaps • Options • = DERIVATIVE INSTRUMENTS • value depends on some underlying asset Derivatives 01 Introduction

  6. Forward contract: Definition • Contract whereby parties are committed: • to buy (sell) • an underlying asset • at some future date (maturity) • at a delivery price (forward price) set in advance • 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 • Buying forward = "LONG" position • Selling forward = "SHORT" position • When contract initiated: No cash flow • Obligation to transact Derivatives 01 Introduction

  7. Forward contract: example • Underlying asset: Gold • Spot price: $380 / troy ounce • Maturity: 6-month • Size of contract: 100 troy ounces (2,835 grams) • Forward price: $390 / troy ounce Profit/Loss at maturity Gain/Loss Gain/Loss Long Short ST ST 390 390 Derivatives 01 Introduction

  8. Derivatives Markets • Exchange traded • 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 • 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 • Europe Eurex:http://www.eurexchange.com/ Liffe: http://www.liffe.com Matif : http://www.matif.fr • United States • Chicago Board of Trade http: //www.cbot.com Derivatives 01 Introduction

  9. Evolution of global market Derivatives 01 Introduction

  10. Global Market Size Source: BIS Quarterly Review, June 2006 – www.bis.org Derivatives 01 Introduction

  11. Why use derivatives? • 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 Derivatives 01 Introduction

  12. Forward contract: Cash flows • Notations STPrice of underlying asset at maturity Ft Forward price (delivery price) set at time t<T Initiation Maturity T Long 0 ST - Ft Short 0 Ft - ST • Initial cash flow = 0 :delivery price equals forward price. • Credit risk during the whole life of forward contract. Derivatives 01 Introduction

  13. Forward contract: Locking in the result before maturity • Enter a new forward contract in opposite direction. • Ex: at time t1 : long forward at forward price F1 • At time t2 (<T): short forward at new forward price F2 • Gain/loss at maturity : • (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty Derivatives 01 Introduction

  14. Futures contract: Definition • Institutionalized forward contract with daily settlement of gains and losses • Forward contract • Buy  long • sell  short • Standardized • Maturity, Face value of contract • Traded on an organized exchange • Clearing house • Daily settlement of gains and losses (Marked to market) Example: Gold futures Trading unit: 100 troy ounces (2,835 grams) July 3, 2002 Derivatives 01 Introduction

  15. Futures: Daily settlement and the clearing house • In a forward contract: • Buyer and seller face each other during the life of the contract • Gains and losses are realized when the contract expires • Credit risk BUYER  SELLER • In a futures contract • Gains and losses are realized daily (Marking to market) • The clearinghouse garantees contract performance : steps in to take a position opposite each party BUYER  CH  SELLER Derivatives 01 Introduction

  16. Futures: Margin requirements • INITIAL MARGIN : deposit to put up in a margin account • MAINTENANCE MARGIN : minimum level of the margin account • MARKING TO MARKET : balance in margin account adjusted daily • Equivalent to writing a new futures contract every day at new futures price • (Remember how to close of position on a forward) • Note: timing of cash flows different Margin LONG(buyer) + Size x (Ft+1 -Ft) IM -Size x (Ft+1 -Ft) SHORT(seller) MM Time Derivatives 01 Introduction

  17. Valuing forward contracts: Key ideas • Two different ways to own a unit of the underlying asset at maturity: • 1.Buy spot (SPOT PRICE: S0) and borrow => Interest and inventory costs • 2. Buy forward (AT FORWARD PRICE F0) • VALUATION PRINCIPLE: NO ARBITRAGE • In perfect markets, no free lunch: the 2 methods should cost the same. You can think of a derivative as a mixture of its constituent underliers, much as a cake is a mixture of eggs, flour and milk in carefully specified proportions. The derivative’s model provide a recipe for the mixture, one whose ingredients’ quantity vary with time.Emanuel Derman, Market and models, Risk July 2001 Derivatives 01 Introduction

  18. Discount factors and interest rates • Review: Present value of Ct • PV(Ct) = Ct× Discount factor • With annual compounding: • Discount factor = 1 / (1+r)t • With continuous compounding: • Discount factor = 1 / ert = e-rt Derivatives 01 Introduction

  19. t = 0 t = 1 ST–F0 0 Should be equal -300 + ST +300 -315.38 0 ST-315.38 Forward contract valuation : No income on underlying asset • Example: Gold (provides no income + no storage cost) • Current spot price S0 = $300/oz • Interest rate (with continuous compounding) r = 5% • Time until delivery (maturity of forward contract) T = 1 • Forward price F0 ? Strategy 1: buy forward Strategy 2: buy spot and borrow Buy spot Borrow Derivatives 01 Introduction

  20. Forward price and value of forward contract • Forward price: • Remember: the forward price is the delivery price which sets the value of a forward contract equal to zero. • Value of forward contract with delivery price K • You can check that f = 0 for K = S0er T Derivatives 01 Introduction

  21. Arbitrage • If F0 ≠ S0 e rT: arbitrage opportunity • Cash and carry arbitrage if: F0 > S0 e rT • Borrow S0, buy spot and sell forward at forward price F0 • Reverse cash and carry arbitrage if S0 e rT > F0 • Short asset, invest and buy forward at forward price F0 Derivatives 01 Introduction

  22. Arbitrage: examples • Gold – S0 = 300, r = 5%, T = 1 S0erT = 315. 38 • If forward price = 320 • Buy spot -300 +S1 • Borrow +300 -315.38 • Sell forward 0 +320 – S1 • Total 0 + 4.62 • If forward price = 310 • Sell spot +300 -S1 • Invest -300 +315.38 • Buy forward 0 S1 – 310 • Total 0 + 5.38 Derivatives 01 Introduction

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