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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

DerivativesIntroduction

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

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

Derivatives 01 Introduction

slide3
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
Course outline

Derivatives 01 Introduction

derivatives
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
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
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
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
Evolution of global market

Derivatives 01 Introduction

global market size
Global Market Size

Source: BIS Quarterly Review, June 2006 – www.bis.org

Derivatives 01 Introduction

why use derivatives
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
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
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
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
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
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
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
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

forward contract valuation no income on underlying asset
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 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
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
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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