Derivatives and Risk Management (Financial Engineering) An Introduction

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Derivatives and Risk Management (Financial
Engineering)An Introduction

• Craig G. Dunbar
• http//www.ivey.uwo.ca/faculty/CDunbar/Derivatives
  _2003.htm

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The Course

• A course about tools
• understand the structure of basic derivative
  building blocks forwards, futures and options
• introduce models for pricing
• First part of course
• lecture and problem based
• applications are largely trading focused
• exercise SP 500 futures trading simulation

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The Course

• Second part of the course
• case-based applications
• using derivatives to reduce financing costs
• using derivatives to manage risks
• derivatives as real options
• special applications of derivatives pricing (e.g.
  MA)

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Level of Math

• Comfort with math is required but there is no
  complex mathematics (e.g. no calculus)
• Must feel comfortable with symbolic algebra
• e.g. nrm interest rate from time n to m
• Must be comfortable with e and ln
• ea x eb e ab ea / eb e a-b
• ln (a x b) ln(a) ln(b) ln (a / b) ln(a) -
  ln(b)
• ln(ea) a

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Evaluation

• Assignments two exams
• assignments trading simulation report mini -
  projects
• exams problem based
• Alternatives
• A project
• Participation
• only evaluated during case discussions
• counts only if it helps your grade

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What are Financial Derivatives?

• Securities whose value is derived from a more
  fundamental asset
• Securities that exist in zero net supply
• Represent a side bet on the fundamental asset

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The Derivatives World
Exchange Traded
OTC
Structured Embedded
Forwards Options Swaps
Bonds plus Warrants Options
Futures Options
Interest Rate Currency Equity Commodity
Securitization
CMOs
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The Uses of Financial Derivatives

• Speculation
• Play on forecast
• Arbitrage
• Play on mispricing
• Risk Management
• Reduce exposure

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What Fueled the Growth in Derivatives?

• Change in volatility in markets
• Exchange rates became floating
• Active control of interest rates
• commodity prices

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Exchange Rate Volatility
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Interest Rate Volatility
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Commodity Price Volatility
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What Fueled the Growth in Derivatives?

• Globalization
• Revenues in different currencies
• Operating Costs in different currencies
• Liabilities in different currencies
• Technological advances
• Level of computerization
• Modeling abilities
• Regulatory changes
• Changes in transactions costs

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Why is this Area Important?

• The market is massive
• Growth rate in the last 10 years has been between
  30 and 35 percent per year

Source Wall Street Journal
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The Global OTC Derivatives MarketIncludes
Interest rate swaps, currency swaps and interest
rate optionsSource International Swaps and
Derivatives Association (www.isda.org)
Notional principal (U Trillion)
Annual trading (U Trillion)
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The Global OTC Derivatives Market(Trillion U
Source www.bis.org)
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The Global OTC Derivatives Market(Trillion U
Source www.bis.org)
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Annual Futures Options Contract VolumeMillions
of contractsexcludes options on individual
equities Source Futures Industry Association
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Canadian vs. International ExchangesNumber of
contracts traded in millionsSources CDCC annual
report, various web-sites (www.cdcc.ca
www.cboe.com www.cbot.com www.liffe.com)
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Losses and Hysteria

• Metallgesellschaft 1b Oil derivatives 93
• Gibson Greetings 20m Interest Swaps 94
• Procter and Gamble 157m Int. Swaps 94
• Orange County 1.5b Structured Notes 94
• Barings 1.3b Options and Futures 94
• Sumitomo 2.6b Copper Contracts 96

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Continuous Compounding The Determination of
Futures and Forwards Prices
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Simple and Compound Returns

• Suppose initial wealth W0 is invested for n years
  at an interest rate of R per year.
• If interest is compounded annually, the wealth at
  end of n years (Wn) will be
• Wn W0 (1 R)n
• If interest is compounded m times per year, the
  wealth at end of n years (Wn) will be
• Wn W0 1

R
nm
m
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An Example

• W0 1000 n 5 years R 10 per year.
• Compounding once per year
• Wn 1000 (1 0.1)5
• Compounding semi-annually
• Wn 1000 ( 1 0.1/2) 10
• Compounding monthly
• Wn 1000 ( 1 0.1/12) 60

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Continuous Compounding
R
mn

• lim 1 e R n
• From the previous example, compounding
  continuously
• Wn 1000 e 5 0.1
• Generally the relation between initial and
  terminal wealth is
• Wn W0 e R n
• Rearranging, we get
• R ln (Wn / W0 ) n

?
m
m
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Properties of Continuous Returns

• Continuously compounded returns are additive
• Let W0 1000, R 10 over the first year and
  12 over the second year, compounded continuously
• W2
• What was the (continuously compounded) return
  over the two years?
• R

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An Example

• The annualized rate of return on a 3 month t-bill
  is quoted as 5.2
• What is the equivalent continuously compounded
  return?
• Rc

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Pricing Forward Contracts

• Notation
• T time until delivery date in forward contract
  (years)
• S price of asset underlying forward contract
  today
• f value of a long position in the forward
  contract
• today
• F todays forward price
• r risk-free rate of interest per annum today
  with
• continuous compounding for an investment
  
• maturing at the delivery date

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Pricing Forwards No Income on Underlying Asset

• An example
• 90-day Forward contract on non-dividend paying
  stock
• Stock price is 20, 90-day bond yields 4
• What should be the forward price (F)?
• Investment strategy
• Borrow 20 to buy one share of stock
• Enter forward contract to sell one share in 90
  days for a forward price F (Note price today to
  enter contract, f, is 0)

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No Arbitrage

• Suppose that the forward price is 21
• Cash flow at execution of strategy 0
• Cash flow at delivery in 3 months
• Sell stock through forward for 21
• Pay back borrowing and interest
• Profit
• To prevent arbitrage, the forward price F must be
  just enough to pay off the loan
• F

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Valuing Forward Contracts

• Value of contract at the time it is entered into
  is zero
• At other times, the value of the contract, f, is
  given by
• f (F1 F0) e -r T
• where F0 originally negotiated forward price
• F1 current forward price
• Strategy
• borrow (F1 F0) e -r T today, buy contract
  with forward price F0 and sell contract with
  forward price F1
• Cash flow at maturity is zero, so up front cost
  must be zero to prevent arbitrage