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1.Introduction

- Outline of this session
- Course outline
- Derivatives
- Forward contracts
- Options contracts
- The derivatives markets
- Futures contracts

Derivatives 01 Introduction

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

Course outline

Derivatives 01 Introduction

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

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

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

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

Evolution of global market

Derivatives 01 Introduction

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

Forward contract: Cash flows

- Notations

STPrice of underlying asset at maturity

Ft Forward price (delivery price) set at time 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

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 (
- Gain/loss at maturity :
- (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty

Derivatives 01 Introduction

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

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

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

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

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

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

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

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

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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