Title: Derivatives and Risk Management (Financial Engineering) An Introduction
1Derivatives and Risk Management (Financial
Engineering)An Introduction
- Craig G. Dunbar
- http//www.ivey.uwo.ca/faculty/CDunbar/Derivatives
_2003.htm
2The 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
3The 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)
4Level 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
5Evaluation
- 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
6What 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
7The Derivatives World
Exchange Traded
OTC
Structured Embedded
Forwards Options Swaps
Bonds plus Warrants Options
Futures Options
Interest Rate Currency Equity Commodity
Securitization
CMOs
8The Uses of Financial Derivatives
- Speculation
- Play on forecast
- Arbitrage
- Play on mispricing
- Risk Management
- Reduce exposure
9What Fueled the Growth in Derivatives?
- Change in volatility in markets
- Exchange rates became floating
- Active control of interest rates
- commodity prices
10Exchange Rate Volatility
11Interest Rate Volatility
12Commodity Price Volatility
13What 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
14Why 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
15The 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)
16The Global OTC Derivatives Market(Trillion U
Source www.bis.org)
17The Global OTC Derivatives Market(Trillion U
Source www.bis.org)
18Annual Futures Options Contract VolumeMillions
of contractsexcludes options on individual
equities Source Futures Industry Association
19Canadian 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)
20Losses 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
21Continuous Compounding The Determination of
Futures and Forwards Prices
22Simple 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
23An 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
24Continuous 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
25Properties 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
26An 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
27Pricing 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
28Pricing 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)
29No 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
30Valuing 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