kim, gyutai, dept. of industrial engineering, chosun university 1 financial engineering

Kim, Gyutai, Dept. of Industrial Engineering, Chosun University

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Financial Engineering


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What is Financial Engineering?

• Engineering is the practical application of mathematical or scientific principles to solve problems or design useful products and services.

• Engineers of all sorts get similar formal training in mathematics, then move o to their respective specializations.

• The term of “FINANCIAL ENGINEERING” is the use of financial instruments such as forward contracts, futures contracts, swap, and options to restructure an existing financial profile into one having more desirable properties .

• The financial engineers apply their various kinds of knowledge bases on financial economics, mathematics,and Probability & Statistics to the dynamics of security markets for the purpose of structuring, pricing, and managing the risk of financial contracts.


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Factors contributing to the growth of Financial Engineering

• Price volatility

• Globalization of the markets• Technological advances• Quantitative sophistication• Advances in financial theories

• Increased competition

Generating A Great Amount of Risk


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Risk( Any Variation in An Outcome)

• Business risk: born by stakeholders such as shareholders, creditors, customers, suppliers, and governments.

• Financial risk

Sources:

• - exchange rate risk

• - interest rate risk

• - credit risk

• - model risk


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The World Becomes A Riskier Place


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Examples for Restructuring Existing

Financial Profile • Forward SWAP; Combining Forwards with Swaps“If XYZ Corporation intends to issue floating-rate notes in nine months

but wants to lock in today’s fixed rate, it can enter into a nine-month forward swap, with the notional principal and maturity of the swap set equal to that of the expected debt offering.” In nine months, the payments on the swap will begin: XYZ will pay a fixed rate, which was known at origination of the forward swaps, and will receive cash flows based on LIBOR (which XYZ will in turn use to make payments on the floating rate debt)”


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1R

2R

9R

1R

2R

TR

1R

2R

9R

TR

1R

2R

TR

TR

10R

TR

10R

TR

+

=


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•Butterfly Option: It involves positions in options with three different strike prices. It can be created by buying a call option with a relatively low strike price, K1; buying a call option with a relatively high strike price , K3; selling two call options with a strike price, K2, halfway between K1 and K3.

•Generally, K2 is closer to the current stock price.

1K

2K

3K

•Since the butterfly option generates a profit if the stock price stays close to K2, but gives rise to a small loss if there is a significant stock price move in either direction, it is appropriate strategy for an investor who feels that large stock price moves are unlikely.


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Continental Airlines

• In Aug 1990, Iraq invaded Kuwait (Gulf War)• By Oct 1990, jet fuel prices had more than doubled from the pre-invasion price• Continentals fuel costs in the month of Oct 1990 were $81 M higher than in Jun 1990• In Dec 1990, Continental filed for bankruptcy


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World Oil Prices

• In 1986, world oil prices fell 50% and overall energy prices fell 24%

• This greatly impacted oil producers and suppliers of energy equipment

• For example, Dresser Industries supplies equipment to energy producers. In 1985,operating profits were $292 M. In 1986,operating profits were $139 M. Its stock price also fell from $24 to $14.


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Interest Rate Example

U.S. Savings and Loans (S&L)• Basically borrow money from the depositors at a short-term

rate and lend to industry at a long- term rate• In mid-1970s, S&L were borrowing money at a short-term

rate of 6% and lending money at the long-term rate of 10%• A net profit of 4% or $4 M on a $100 M• By 1982, the short-term rate was 12% and the going long-

term rate was 11%• A loss of 1% or $1 M on a $100 M amount• In a period of five years, S&Ls went from making $4M to

losing $1 M on its loans


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Risk Management Defined

• Risk management does not mean risk elimination Instead it implies a structured approach to minimize

risks impacting a firm’s bottom line• Risk management has evolved from the inability of economists to forecast market prices Market prices have been more volatile since 1970 In an efficient market it is nearly impossible to forec

ast


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Three Different Levels of Market Efficiency

1. Weak-form efficiency states that current market prices reflect all market (or public) information to include historical prices, rates of return, etc.

2. Semistrong-form efficiency encompasses weak-form and states that market prices adjust rapidly to the release of new public information

3. Strong-form efficiency states that market prices

reflect all private and public information


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Forecasting in an Efficient Market

• It is assumed that weak and semistrong-form efficiency hold• Implies current market prices reflect all available public inform

ation• Because historical prices will not change the price, the only ev

ent that will change prices is the release of new information• However, new information is unknown and arrives in a random f

ashion• Hence, accurate forecasting in an efficient market would requir

e predicting the arrival of unknown information – a near impossib

ility!!• Therefore, companies engage in risk management practices


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Risk Management Practices

• A company can use derivative securities

– Forwards- to exist as early as the 12th century

– Futures - to exist as early as the 16th century

– Swaps – dated from the public announcement of the currency swap

between IBM and the World Bank in 1981. – Options- to exist as early as the 17th centuryDerivatives are financial instruments that derive their value from the prices of one or more other assets such as equity security, fixed-income securities, foreign currencies, or commodities.


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Derivative Products

• In June 2000, the estimated global notional size of derivatives was $104 trillion.

• Swaps – 60%• Forwards/Futures – 20%• Options – 15%• Other – 5%


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Derivative Products

• Forwards, Futures, Swaps, Options

• Derivatives can be held long or short

– Long: Buy the asset – Short: Sell the asset• Spot price = Current market price


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Three Different Types of Traders

• Hedgers• Speculators• Arbitrageurs


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Hedgers

• Hedgers utilize derivatives to proactively manage risks affecting the firm’s core business.

– Farmers hedge the risk associated with their crops by entering into futures to sell their crop before they harvest it.

– Mutual fund managers will hedge the risk associated with a downturn in stock prices.

– Banks hedge interest rate risk by entering into either long/short interest rate derivatives.


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Speculators

• These investors try to take a position in the market. They are betting that a price will move either up or down from its current position.

• This is a high risk, high reward approach to investing.“ Assume you think that the current price of corn per bushel

ishistorically high, and you think corn prices will fall (i.e. youwill take a short position). The futures price 6 months fromnow of corn is $3 per bushel, and one contract requires 5,000bushels. Let’s say that your hunch is correct, and the spotprice of corn is $2 per bushel in six months. The profit fromyour hunch is equal to $5,000.”


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Arbitrageurs

• These investors look for disparities in market prices of compatible assets.

• Then arbitrageurs can lock in a profit by simultaneously entering into two or more transactions.

• The arbitrage profit is what drives a fair market of value of derivative products.


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Forwards

• A forward contract is an agreement to buy or sell an asset at a particular time in the future for a certain price (called the forward price).

• Firms that intend on buying the asset enter into a long position, whereas firms intending on selling an asset enter into a short position.

• At expiration, a long forward position has the payoff (S – F) and a short forward position has the payoff (F – S) [where S = Spot price and F = Forward price]


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Forward Payoff


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Short Forward Example

• An entrepreneur plans on selling his gadget six months from now and wants to hedge against the possibility of a significant drop in gadget prices. The forward price for gadgets is $3 per unit – which implies that the entrepreneur has a contract to sell his gadgets for $3 six months from now. Because the entrepreneur plans on selling his gadgets, he will enter into a short position• No matter what happens to the price of gadgets in the future, the entrepreneur will sell it

for $3 per unit.• Assume the price is $4 per gadget six months from now. The entrepreneur will lose $1 with the forward contract [i.e. the payoff is (F – S) = (3 – 4) = –1]• But it will make an additional $1 by selling at the spot price – for a net gain of zero.• If the price is $2 six months from now, then the entrepreneur will gain $1 from the forward (i.e. the payoff of the forward is +1), but lose $1 from the spot price – for a net gain of zero.


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Another Example for A Forward Contract

• A long forward contract on a non-dividend-paying stock was entered into some time ago. It currently has six months to maturity. The risk-free rate of interest (with continuous compounding) is 10% per annum, the stock price is $25, and the delivery price is $24. In this case, So=25, r=10%, T=0.5, and K=24.

• The six-month forward price, F0, is given by

• The value of the forward contract is

0.1 0.525 $26.280 0

r TF S e e

0.1 0.5(26.28 24) $2.170

f e


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Forward Exchange Rate

Example• A forward foreign exchange dealer working for Woori Bank being asked by a US client to qu

ote a rate for wons against a dollar, for delivery one year after spot. • The customer wants to buy exactly 1,254,000 won from the bank in order to settle an acco

unt that will be payable at that time• So the bank will be selling 1,254,000 won and receiving dollars.• The questions to be resolved are 1. How may dollars should a bank receive in exchange for the won? 2. What is the fair exchange rate for $/won one year forward?• Suppose that a spot rate is 1,200 won/dollar. One year dollar interest rate is 2% and one year won interest rate is 4.5%.


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spot

1 yr -1,254,000

US Won

a) The original deal

?

spot

1 yr -1,254,000

+1,254,000

US Won

b) Hedge the forward won

-1,200,000Lend won @ 4.5%

?

spot

1 yr -1,254,000

+1,254,000

US Won

c) Hedge the spot won

+1,200,000-1,200,000

Lend won @ 4.5%

?

-1,000Sell US spot @ 1,200

spot

1 yr -1,254,000

+1,254,000

US Won

d)forward transaction completely hedged

+1,200,000-1,200,000

Lend won @ 4.5%

+1,000 -1,000

Sell US spot @ 1,200

+1,020-1,020 Sell won fwd @1,229.4


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Formula for Forward Exchange Rate

• $ * Spot * (1 + iq) = $ * (1+ib) * F• 1,000 * 1,200 * (1+0.45) = 1,254• 1,000 * (1+0.02) * F =1,020F• 1,254 = 1,020 F• F=1,229.4won/dollar

1

1 ( )

i tqF Si tb


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Forward Contract Attributes

• Money is only exchanged at the expiration of the contract.

• Forwards are custom-made to be agreed upon by only the parties involved.

• Significant default risk because you must rely on the other party to ‘pay-up’

• Not very liquid (i.e. difficult to find someone else to enter into your agreement)

• –Most financial assets are not traded in forwards – usually foreign exchange risks between large reputable firms.


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Futures• A futures contract is an an agreement to buy or

sell an asset at a particular time in the future for a certain price

(called the future price).• Firms that intend on buying the asset enter into a

long position, whereas firms intending on selling

an asset enter into a short position.• At expiration, a long future position has the payoff

(S – F) and a short future position has the payoff (F – S) [where S = Spot price and F = Forward

price]


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Futures Payoff


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Example• It’s early January and a major industrial

corporation knows that it will need to buy 1,000 barrels of oil in December.

• It’s concerned about the price it will have to pay in December it buys oil futures at F0=$19.45 in January.

January Income

Long Futures at F0 0

December Income

Close out Future FT – F0 = ST – F0

Buy Oil -ST

-F0= -$19.45


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Observation

• The futures trading has perfectly hedged its risk

• Note that FT = ST, spot price at expiration.


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Basis Risk

• Suppose that it actually wanted to buy oil in November, but couldn’t find a November contract.

- it unwinds its position in November. January Income

Long Futures at F0 0

November Income

Close out Future FT-1 – F0

Buy Oil -ST-1

-$19.45+(FT-1 – ST-1)


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• A basis risk is incurred due to the mismatch between the contract maturity and we need to transact.

• A basis risk of (FT-1 – ST-1) is uncertain in January, while F0=$19.45 is certain at the time.

Observation


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Hedging with futures

• If an company knows that it has to sell a particular asset at a particular time in the future, it can hedge by taking a short position, therefore locking in the price of delivery.

• This is called a short hedge. • Similarly, a company that knows that it will need an

asset in the future can take a long hedge, thus locking in the price of purchase.

• It is very important to note that hedging does not necessarily improve the financial outcome, it just reduces the uncertainty.


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In practice, hedging is not perfect, the basis risk arises due to a number of

reasons, some of which were discussed in the introduction:

• The asset being hedged might be different that the one underlying the futures contract, i.e. using a 30y T-bill to hedge a 10y T-note;

• The hedger might be uncertain about the exact time that the delivery has to take place, i.e. a new oil ring that is expected to start extracting next summer, without knowing exactly when; and

• The futures contract matures after the delivery date that the hedger has in mind, i.e. the hedger needs to buy steel in January but steel futures expire on March.


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• is the spot price of the underlying asset • is the price of the futures contract that

has been utilized.• If the asset to be hedged is the same as

the one underlying the futures, then the basis on expiration is equal to zero.

• If the delivery date is not the same as the one that the futures matures, then the basis will signify the ``losses'' or ``gains'' of the hedge than are not known when the hedge is constructed.

( ) ( ) ( , )b t S t F t T

( )S t

( , )F t T

If negative, a market is normal

If positive, a market is inverted


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Example(Basis Risk: Different Maturities)

• Today, the gold price is

• Say that one has to deliver gold at time

• and in order to hedge takes a short position on a futures contract that matures at time

• The price of this contract is equal to

• And the basis today is

• The basis on the delivery date will be

is


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b(t)

F

S

t T

b( )

Basis Risk


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Observation• At time the company will close the futures contract by taking a

long position and at the same time sell the gold at the current price of S().

• The marking-the-market procedure will leave the company with a

loss of F( ,T) – F(t,T) since the futures was sold at time t and bought at time .

• While by selling the asset the income is S().

The total income is therefore

S() + F(t, T) – F(,T)=F(t,T) + b()

• The value F(t,T) is known at time t.

•While the quantity b() represents the basis risk.

•Obviously, if =T, then b()=b(T)=0, and there is no basis risk.


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Pricing of Futures• Consider Two Ways of Getting The Asset , e.g. gold in the future. A: go long position in a gold future - the futures price is F0

B: borrow money and invest it directly in gold - gold price is S0

Cash Flows: Initial At Maturity A 0 ST – F0

B 0 ST – S0(1+r) By arbitrage, it must be that: ST – F0 = ST – S0(1+r)

F0 = S0(1+r) Forward Price = Spot Price (1+r)


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Arbitrage Opportunity

• If F0 > S0(1+r), we can make free money.

Initial Borrow Money S0

Buy Gold -S0

Short Gold Future 0 0 At Maturity Pay Back Loan -S0(1+r)

Sell Gold ST

Close Out Future F0 - ST

F0 – S0(1+ r) >0


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Future Contract Attributes

• Traded on an exchange - guaranteed performance which reduces default risk

• Standardized terms and conditions• Marked to market daily• Requires money at the outset to enter into

future contract – usually a percentage of the total contract amount termed a margin account

• The majority of futures contracts do not lead to delivery – instead the positions are closed out prior to maturity


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Convergence of Futures Price to Spot

Price


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Forward Vs. Futures Contract

표 1

Characteristics Forward Futures Standarzied Contract (delivery date, quality, quantity)

No Yes

Where to be traded counter

Over- the Counter

Organized Exchanges

Credit Risk Yes No Clearinghouse No Yes Settlement End of The

Contract Marked- To-Market

Margin Requirement No Yes Transaction Cost High Low Position to be cancelled Difficult Easy Regulations No Yes


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Summary of Results for A Contract with Time To Maturity T on An Investment Asset with Price S0 When The Risk-Free Interest Rate for A T-Year Is r.표 1

Asset Forward /Futures Price

Value of Forward Contract with “K”

Provides No Income Provides Known Income with Present Value I Provides Known Yield “q”

S0e

rT

(S0- I)erT

S0e

(r- q)T

S0 –Ke- rT

S0- I- Ke- rT

S0- e- qT- Ke- rT


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Swaps

• A swap is an arrangement between two parties (with or without an intermediary) to exchange some specified cash flow at specified intervals in the future.

• A popular swap is the interest rate swap to

transform a liability.


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Swap Example

• Suppose two firms plan on financing a new project.• Firm A currently has a fixed-rate loan, but would like to

transform it into a floating-rate loan.• Firm B currently has a floating-rate loan, but would like

to transform it into a fixed-rate loan.• Assume the following information: – Firm A pays 6.4% on its $100,000 loan – Firm B pays LIBOR plus 0.5% on its $100,000 loan – Firm A and Firm B agree to a swap where Firm A

pays LIBOR to Firm B and Firm B pays a fixed 6% to Firm

A.


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kim, gyutai, dept. of industrial engineering, chosun university 1 financial engineering

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