financial engineering is a multidisciplinary field involving financial theory

8/3/2019 Financial Engineering is a Multidisciplinary Field Involving Financial Theory

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Financial Engineering is a multidisciplinary field involving financial theory, the methods ofengineering, the tools of mathematics and the practice of programming. The Financial EngineeringProgram at Columbia University provides a one-year full-time training in the application ofengineering methodologies and quantitative methods to finance. It is designed for students whowish to obtain positions in the securities, banking, and financial management and consultingindustries, or as quantitative analysts in corporate treasury and finance departments of generalmanufacturing and service firms.

Financial engineering is a process that utilizes existing financial instruments to create

a new and enhanced product of some type. Just about any combination of financial

instruments and products can be used in financial engineering. The process may

involve a simple union between two products, or make use of several different

products to create a new product that provides benefits that none of the other

instruments could manage on their own.

One excellent example of financial engineering is financial reinsurance. Companies

that offer reinsurance options essentially provide a way for the ceding insurer to

minimize a drain on available resources when a major shift in premium growth or

reduction is taking place. In this scenario, the process of financial engineering helps

to create a stable environment that will allow the insurer to remain solvent and

stable even when extreme conditions exist.

For the consumer, the work of a financial engineer to create new finance product

offerings can be a great advantage. In some instances, the new and improved

product is simply a repackage of several independent but complimentary products

made available at a lower price. For example, the consumer may find that purchasing

insurance coverage that provides dental, hospital, and prescription coverage may be

significantly less expensive than purchasing individual plans.

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Read more: Financial Engineering - benefits, expenses

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Financial engineering is the design and construction of a new financial contract or

the packaging of existing financial instruments to meet very specific risk and

return requirements of the client. It is analogous to the engineering function in

building construction. For example, the building construction contract may includespecifications regarding size, number of rooms, adequate plumbing and heat, quality

of materials to be used, and a completion date. The financially engineered contract

may also include specifications of size (or dollar amount), the types ofsecurities

that will be used, the cash flows that they will generate, the risk associated with those

cash flows, and the date upon which the contract will be renewed or expired.

This very general definition of financial engineering includes many contracts that are

now considered commonplace. For example,banks sustained large losses in the

early 1980s when their cost of funds rose sharply with interest rates. These banks

had made large, long-term, fixed interest rate loans to families purchasing homes.

The banks found, however, that the moderate fixed interest charges they received on

these loans was not sufficient to cover the interest expense that was incurred to

attract new funds to the bank. Hence, banks began to write adjustable-rate loans that

would vary interest charges to borrowers commensurate with fluctuations in the cost

of funds to the bank.

Another common example of financial engineering is the mutual fund. Individual

investors realized that there were benefits in terms of risk reduction if they could

invest in a broad array of securities. Most individuals, however, had limited resources

and found it very expensive to purchase small amounts of many securities. A basic

mutual fund is a portfolio of securities that can be as diverse and numerous as the

client demands. The creation of these funds allowed individuals to purchase shares ofan already diversified portfolio and establish an investment with lower risk, and at a

more moderate cost than they could achieve otherwise.

The two previous examples illustrate the ubiquitous nature of financial engineering.

Financial contracts that are now considered standard were designed and constructed

to meet the needs of a particular set of clients. Financial engineering still responds to

those needs but now frequently incorporates more complex combinations of

securities, including foreign currencies and derivative securities. Beforedescribing some of these more complex examples of financial engineering, a brief
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review of the fundamentals of the individual elements that are used in their

construction is useful. This review begins with basic financial assets themselves:

stocks, bonds, and various indexes. This will be followed by a description of

various derivative securities. Derivative securities are so named because their value isderived from the value of another security. Options, forward contracts, and futures

contracts are in this category.

BASIC FINANCIAL ASSETS

BONDS

Shares of stock and bonds represent claims on current and future earnings of a

corporation. Bonds represent a debt or liabilityon the corporation's (or

government's)balance sheet and typically oblige the firm to make periodic interestpayments to bondholders. Bonds eventually mature and at that time the principal

amount of the loan that the bond represents must be returned to the holder. The

holders of a bond may passively collect interest payments over the duration of the

bond's life and then receive the principal at maturity. The holder may also elect to sell

the bond at any time prior to maturity. Since the bond represents a claim on a series

of future payments, the bond's value can be estimated at any time as the discounted

present value of those remaining payments. Thus, when the bondholder offers the

bond for sale, the interest rate used to discount the remaining payments will be the

primary determinant of its value. This interest rate can also be interpreted as the

potential buyer's required rate of return. This required rate will be determined by a

variety of factors including expectations of inflation, the default risk associated with

the corporation, and interest rates offered on similar securities. This description

culminates in two observations regarding the value of bonds. First, the higher the

required rate of return, the lower the discounted value of the bond's required

payments and hence, its value. In other words, as interest rates go up, bond prices godown. Conversely, as interest rates fall, bond prices rise. Second, these interest rates

are determined in a competitive market and they will fluctuate continuously.

Therefore, the market value of the bond will change constantly.

STOCKS.

Stock represents a claim on residual earnings of the corporation. Since there may be

no earnings available after all other claims have been satisfied and since those

earnings may be retained by the firm rather than directly distributed to stockholdersas dividends, the value of stock is inherently more volatile than the value of bonds.
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The value of stock is also related to the expected future cash flows: dividends and

future selling price. These future cash flows, however, are much more difficult to

forecast. Obviously, as the market's assessment of the level of these future cash flows

improves or deteriorates, the stock's price will rise or fall.

MARKET INDEXES.

There are also a variety of market indexes that measure overall price movement of the

U.S. stock market (e.g., Dow Jones Industrial Average, Standard & Poor's 500),

interest rate sensitive instruments such as bonds (e.g., Salomon Brothers Bond

Indexes), and the level of interest rates themselves (e.g., yields on various securities

issued by the U.S. Treasury, the Federal Funds rate, and the London Interbank

Offered Rate, or LIBOR). There are comparable indexes for every major financialmarket throughout the world (e.g., the Financial Times 100 in the U.K. and the

Nikkei Index in Japan). These market indexes play an important role in financial

engineering. Contracts can be tied to the value of a specific index and can thereby be

used to initiate cash flows between contracting parties. In this way, a contract can

simulate rates of return for an index without the obligation to buy and hold the

securities actually included in the index.

DERIVATIVE SECURITIES

Stocks, bonds, and market indexes represent the fundamental set of building blocks

that can be used to engineer a financial contract. Such derivative securities as

options, forward contracts, and futures contracts comprise the next level.

OPTIONS.

An option is a contract that provides the holder with the right to purchase or sell a

security at a predetermined price regardless of the prevailing market price. To obtain

such a contract, the potential holder must buy it from a seller who has assessed the

risk associated with the potential gains and losses on the contract. The option to buy

is referred to as a call and the option to sell is a put. For example, suppose an

individual paid $5 to purchase a call option on XYZ stock with an exercise price of

$60 and the stock subsequently rose to $72. This individual could exercise the option

to buy at $60 and, ignoring brokerage fees and taxes, resell the stock for $72 for a

gross profit of $12. When the initial cost of the option is factored in, the net profit to

the call buyer is $7. If XYZ's price had gone higher the profit would have been evengreater. On the other hand, if XYZ's price had fallen to $57, the call buyer would not


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elect to exercise the right to buy at $60. The maximum loss at any price below $60

would be limited to the initial cost of the option, $5 in this case. So, the call option

buyer has unlimited potential for gains while losses are limited to the price, or

premium, initially paid. Conversely, the seller of the option has limited gains, but thepotential for significant losses.

Contrast the position of the call buyer with that of the put buyer. Suppose an

individual buys a put option on XYZ's stock for $4 with an exercise price of $60. This

individual now has the right but not the obligation to sell XYZ for $60. If the price

falls to $55, the put holder can buy the stock in the market and sell it for $60 by

exercising the put option. This produces a gross profit of $5 and a net profit of $1

when the original put premium is factored in. The gains to the put buyer will increaseas the value of XYZ continues to fall, but will diminish if the price rises. If the price is

above the exercise price of $60, the put buyer will not exercise the option and will

incur a net loss of $4, the amount of the put premium. Therefore, the put buyer has

significant potential for gains if XYZ's stock price falls significantly, but losses are

limited to the amount of the put premium. Again, the converse is true for the put

seller. The seller incurs significant losses if XYZ's value falls materially, but gains are

limited to the amount of the premium.

Since there must be a buyer for every seller, both must agree to the initial price or

premium. This premium will be influenced by the difference between the current

price for the stock (or other asset) and the exercise price on the contract. Options are

essentially a "zero-sum" game. This means that what the buyer gains, the seller loses.

Only one party to the contract will have made the proper assessment. Both parties,

however, will agree that stocks with greater potential for large price movements are

worthy of higher option premiums than those with more stable prices. Also, options

have an expiration date and buyers are willing to pay more for an option that has

longer to live.

While these examples have centered on stock options, there are also many actively

traded contracts on various government bonds, market indexes, commodities (e.g.,

corn, oil, gold), and foreign currencies.
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FORWARD CONTRACTS AND FUTURE CONTRACTS.

Forward and futures contracts are typically derived from price levels for various

market indexes, interest rate sensitive securities such as bonds, commodities, and

foreign currencies. These contracts are designed to transfer the risk associated withthe price level of the underlying asset from one party to the other. Forward contracts

represent an agreement to make or take delivery of a specific asset at a specific future

date for a price that is also predetermined. For example, suppose A, a U.S.

businessperson, has an obligation denominated in French francs (Fr) that is due in

six months. A's major concern is that the dollar will weaken with respect to the franc.

If the current rate of exchange is $0.20 per Fr, then a weaker dollar will produce an

exchange rate of, say $0.22 per Fr in six months. This means that A will have to pay

more dollars for the same number of francs. Conversely, if the dollar strengthens and

the exchange rate moves to $0.18 per Fr, then A can meet the franc denominated

obligation with fewer dollars. A's concern is exchange rate risk. One way to avoid this

risk is to buy French francs on the forward market. Suppose that A can enter into an

agreement to take delivery of the necessary francs in six months for a price of $0.21

per Fr. That forward price is fixed, eliminating exposure to subsequent fluctuations in

the exchange rate, favorable or unfavorable. This practice is referred to as hedging.

Who will sell the French francs to A using the forward contract? There are two

possibilities. B is a French businessperson who has an upcoming obligation

denominated in U.S. dollars. B is also subject to exchange rate fluctuations and may

be willing to sell francs at $0.21 per Fr in six months. B's willingness to sell francs can

also be interpreted as an interest in buying dollars in the forward market. In this

example, both A and B are hedging to eliminate exchange rate risk. If B is not

interested or available to accept the other side of this contract, there is another

possibility. C is a speculator in exchange rate movements. C believes that the currentrate of $0.20 per Fr will be stable for the next six months and is therefore willing to

agree to sell to A at $0.21 per Fr in six months. Again, A has eliminated concern with

exchange rate fluctuation. C expects to be able to buy francs for $0.20 and sell them

to A for $0.21 earning $0.01 per franc. If the rate rises to $0.22 per Fr, C will lose

$0.01 per franc. If the dollar strengthens, however, and the rate falls to $0.18 per Fr,

C will earn $0.03 per franc. C is willing to speculate on the future exchange rate of

dollars for francs. Exchange rate risk has not been eliminated, only transferred from

A, the hedger, to C, the speculator.


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While forward contracts can be customized to meet the very specific needs of theparties involved, they also create counterparty risk. Counterparty risk is an important

underlying concept in all financially engineered contracts. It represents the potential

that one of the parties to the contract will not follow through on its obligation. For

example, if A entered into a forward contract to purchase five million French francs

from C six months from now and C failed to deliver, A would be obliged to purchase

the necessary francs at the prevailing market price. Conversely, after six months, A

may find that the market price for French francs is favorable to the price specified in

the forward contract and renege on the promise to purchase from C. Though the

contract itself can (and does) penalize each party for deviations in promised

performance, it may be inconvenient and costly to enforce these provisions.

Futures contracts are similar to forward contracts in that they represent an

agreement to engage in a transaction at some future date. Futures contracts, however,

are standardized with respect to size, expiration date, and many other relevant

features. This means that hedgers may not be able to obtain the exact contract

parameters to completely eliminate risks associated with price movements. It also

means, however, that buyers (who agree to take delivery of an asset) and sellers (who

agree to make delivery) of futures contracts are pricing identical contracts. This

allows all trades to be funneled through a clearinghouse that can assume all

counterparty risk. It also means that traders can quickly purchase or sell additional

contracts to perfect a hedged position or to amplify a speculative one. Likewise,

positions in the futures market can be "unwound" by selling contracts to offset

previous purchases or by buying contracts to offset previous sales.

Another important distinction between forward and futures contracts regards the

timing of the cash exchange between the parties. In a forward contact, the cash flow

from the buyer to the seller of the asset occurs at the end of the contract period. With

a futures contract, the buyer and seller agree on a price for future delivery at a

particular time, but that future price is changed continuously. If the price for future

delivery rises in a given day, the buyer is now holding a claim that is more valuable

than it was previously. The seller now finds it more costly to fulfill the contract. To


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adjust for this change, an amount equivalent to the aggregate change in value is

transferred from the seller's account to the buyer's account. Likewise, if the price for

future delivery falls during the day, funds are transferred from the buyer's account to

the seller's account. This process is repeated daily for the life of the contract and iscalled "marking to market." As a result, at the contract's expiration, all favorable or

unfavorable movements in the market price of the asset to be delivered have already

been accounted for. If the buyer of the contract opts to take delivery of the asset at

this point, the transaction occurs at the prevailing market price.

The derivative securities discussed previously can correctly be considered as products

of financial engineering. These contracts were invented and in some cases

standardized in order to provide clients with a more effective vehicle for avoidingparticular types of risk or of speculating on specific price movements. In the next

section, these securities will be included as some of the primary building blocks for

more complex financially engineered contracts.

COMPLEX FINANCIAL ENGINEERING

CONTRACTS

PORTFOLIO INSURANCE.

One prominent example of financial engineering to meet the needs of clients is

portfolio insurance. Portfolio insurance is essentially a strategy of hedging,

stabilizing, or reducing the downside risk associated with the market value of a

portfolio of financial assets such as stocks and bonds. There are a variety of

techniques to protect the value of such a portfolio.

As an example, suppose a portfolio manager wants to build a floor under the current

value of a well-diversified portfolio. Furthermore, suppose that this portfolio iscurrently valued at $1,594,000, and its changes in value closely correspond with

changes in the Standard & Poor's 500 (S&P 500) index. Ideally, the manager would

like to reap the benefits of further increases in portfolio value, but wants to assure

investors that the value will not fall below a certain, specific level. One solution is to

purchase put options on the S&P 500 index. These options are heavily traded at a

variety of exercise prices. If the current level of the S&P 500 index is 1,225.50 and the

manager wants to ensure that the value of his portfolio does not fall by more than 10

percent, put contracts with an exercise price of 1,110 (approximately 10 percent below


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the current level) can be purchased. The manager must purchase enough put option

contracts so that the underlying value of the optioned asset is equal to the value of the

portfolio. In this example, the portfolio value is approximately 1,300 times the

current value of the S&P 500 index. Therefore, if the manager could buy puts on1,300 "units" of the index, the position could be fully hedged. In reality, a single S&P

500 put contract represents 500 units of the index. So, the manager would purchase

three put contracts. Subsequent to the purchase, if the S&P 500 index (and the

portfolio) rises in value, the manager will not exercise the put. Gains to the portfolio

will be reduced by the modest amount of the put premium that was paid. On the

other hand, if the index and the portfolio dropped in value by 20 percent, the put

could be exercised at a significant profit that would generate a combined net loss for

the position of approximately 10 percent. If the index value fell even lower, the profit

from the put would be even greater and always provide a net loss of 10 percent.

Other techniques of portfolio insurance use futures contracts on stock and other

market indexes. In the previous example, the manager could "synthetically" sell some

or all of the portfolio by selling futures contracts on the S&P 500 index. If the

portfolio subsequently fell in value along with the S&P 500 index, the futures position

would generate prohits that would partially or entirely offset the loss. If market prices

rose, the portfolio would rise in value but the futures position would generate a loss

that would tend to offset the gain. Note that this technique not only stabilizes the

value of the stock portfolio, but also allows the manager to create a position with

profits and losses that is equivalent to a smaller stock portfolio. This lower risk

position is achieved without the significant expense of actually selling a portion of

each individual stock position within the portfolio. Technically, this is an example of

hedging, or maintaining a particular market value for a period rather than ensuring aminimum value while retaining the opportunity for upside gains. It is possible,

however, to sell the proper number of S&P 500 index futures in order to mimic the

overall profits of the put insured portfolio described above. This would require

periodic adjustment to the hedge, or the number of futures contracts sold, as prices

changed and the time to expiration of the contracts diminished.

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SWAPS.

Another broad category of contracts that result from financial engineering are

referred to as swaps. Swaps represent exchanges of cash flows generated by distinct

sets of assets or tied to distinct measures of value. An early example of an engineered

swap is the currency swap. In this example, consider two firms in different countries

each having continuing financial obligations in the other's country. More specifically,

consider a French firm with a U.S. subsidiary that requires dollars to operate and a

U.S. firm with a French subsidiary that has need for French francs. One alternative isto borrow the funds in the home country and exchange them for the foreign currency

needed by the subsidiary. Another alternative is for the subsidiary to borrow the

needed funds in the local currency. This second alternative will provide needed funds

for the subsidiary and avoid the costs associated with foreign exchange transactions.

It is also likely, however, that the subsidiary is at a disadvantage when negotiating the

rate on a loan in the local currency. For example, the U.S.-based subsidiary of a

French corporation may not have the perceived creditworthiness of a U.S.

corporation with foreign subsidiaries and as a result will be forced to pay a higher

rate of interest on the dollar-denominated loan.

If each firm becomes aware of the other's needs, they can do the following. First, each

parent corporation should borrow an equivalent amount in their home currencies.

These amounts will be equal based on the current exchange rate between dollars and

francs. Second, they will simultaneously transfer the proceeds of the loan to the other

firm's subsidiary (i.e., the French parent will transfer the borrowed francs to the U.S.

firm's French subsidiary, and the U.S. parent will transfer the borrowed dollars to the

French firm's U.S. subsidiary). As interest payments become due, the French-based

subsidiary pays the French parent and the U.S.-based subsidiary pays the U.S. parent.

Finally, when the term of the loans expires, each subsidiary will repay the other's

parent. Note that this financially engineered contract has (I) effectively exploited each

firm's ability to borrow at more favorable rates in its home country and (2) avoided

all need for foreign currency exchange.
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Obviously, the crucial factor in the formation of such a mutually advantageous

contract is the identification of two parties with offsetting needs. In recent years,

many financial intermediaries have developed services to fill this need. Swap dealers

and brokers have developed the expertise to serve a broad variety of needs bymatching the interests of counterparties and by engineering contracts that are

mutually advantageous to the contracting parties and profitable for the intermediary.

A second common swap agreement is the interest rate swap. This typically takes the

form of an exchange of a fixed-rate interest payment for a floating-rate interest

payment. Suppose a bank has made a large number of loans at a fixed rate, but most

of its liabilities are floating-rate obligations. If interests rise materially, its expenses

will rise but its revenues are fixed. Profitability will suffer. If the bank can swap its 9-percent fixed-rate loans for a comparable amount of floating-rate obligations that

generate the yield on 30-year U.S. Treasury bonds plus 4 percent, it has materially

reduced the influence of interest rate fluctuations on its profitability. In this example,

once the bank has found a willing swap partner, the parties will agree to a notional

principal amount. That is, the counterparties will agree on the amount of interest-

generating capital that will be used to design the agreement. Typically, the parties will

not exchange these notional amounts because they are identical. As time elapses, the

bank will swap interest payments with its counterparty. For example, if the Treasury

bond rate is 6 percent during a particular period, the agreement mandates that the

bank receive 10 percent while it pays 9 percent. The swap agreement will require only

that the net difference be exchanged, I percent paid to the bank in this case. If the

Treasury bond rate drops to 4.5 percent, then the bank is obligated to pay the net

difference between 8.5 percent (or 4.5 percent + 4 percent) and 9 percent, or 0.5

percent to the counterparty. If the Treasury bond rate remains at 5 percent, the fixed

and floating rates are equivalent and no cash exchange would be necessary. Sincethere was no need for an actual exchange of the identical principal amounts at the

beginning of the swap, none is required to close the positions at expiration of the

agreement.

More complex swaps could involve trades of fixed- and floating-rate payments

denominated in different currencies. Others could involve swaps of the income from

debt instruments for the income generated by an equity investment in a specific

portfolio such as the S&P 500. Swaps can also provide the basis for engineering amore efficient method of diversifying risk or allocating assets across asset classes.


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Consider this well-documented example. Achief executive officer (CEO) of a

major corporation has accumulated a significant equity stake in his firm. While the

CEO has other investments, he is not effectively diversified since he has an enormous

amount of his own firm's stock. The CEO can contact a swap dealer who will arrangeto swap the cash flows generated from the CEO's stock(capital gains and/or

dividends) for a cash flow generated by an identically valued investment in a broadly

diversified portfolio or market index. In this example, the CEO has (1) avoided the

cost of selling his stock and any capital gains taxes that may result from the sale; (2)

retained the voting rights of his stock; and (3) created a "synthetic" portfolio that is

much less sensitive to the fluctuations in value of any particular company.

The swap can be engineered to provide immediate international diversification.Suppose two portfolio managers, one in the United States and another in Japan,

manage purely domestic portfolios. They may agree to swap notional values that

would generate returns on their own managed portfolios or generate cash flows

commensurate with an investment in a market index. For example, the U.S. manager

may agree to provide the cash flow generated by a $100 million investment in the

S&P 500 in exchange for returns generated from a similar-sized investment in the

Nikkei 225 index. This would provide instant international diversification without the

sizable cost of purchasing a large number of individual foreign securities. In addition,

many countries impose fees or taxes on returns to foreign owners. A properly

engineered swap agreement can avoid most or all of these expenses.



Engineering.html#ixzz1YPKYkdqR

OTHER FINANCIALLY ENGINEERED

INSTRUMENTS

There are a myriad of other examples of new financial instruments or contracts.

Many of these instruments are new and trade infrequently. They are often referred to

as "exotics." For example, it is possible to use combinations of puts and calls on

interest rate instruments to create caps, floors, and collars on interest payments. Acap represents the maximum rate that a floating interest rate position can obtain, a
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floor is the minimum rate, and a collar is the combination of a cap and a floor.

Another unusual option feature is the lookback option. A call option with the

lookback feature allows the holder to purchase the asset at the most favorable

(lowest) price that prevailed over the life of the option. A put option with this featureallows the holder to sell the asset at the highest price over the option's life. These

options set the exercise price at the end of the option's life rather than at the

beginning. Closely related are Asian, or average-rate options. These options set the

exercise price at expiration as the average asset price during the option's life span.

Barrier options are options that are activated, canceled, or exercised if a particular

price condition is met. For example, a "down and out" option is canceled if the asset

price falls below the exercise price, while a "down and in" option is activated if the

same price trigger is breached. Conversely, "up and out" and "up and in" options are

canceled or activated when the exercise price is exceeded. Since these options are

inert for large ranges of their underlying asset's price, they are less expensive than

ordinary options and have generated interest among hedgers and speculators.

In summary, financial engineering is the design and construction of new financial

contracts. These contracts are typically assembled from a modest number of basic

financial instruments and indexes including stocks, bonds, options, forward

contracts, and futures contracts. The need for properly engineered financial contracts

is motivated by the client's interest in reducing risk, reducing costs associated with

foreign exchange or other market transactions, and to provide the potential to

enhance returns. Many financial intermediaries have developed specialized services

in the area of financial engineering. As they have done so, the markets where

elaborate and specialized contracts can trade efficiently have expanded and are likely

to continue to do so.



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[ Paul Bolster ] SEE ALSO KOL DND PUT OPTION
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FURTHER READING:

Jarrow, Robert, and Stuart Turnbull.Derivative Securities. Cincinnati:

SouthWestern, 1996.

Smithson, Charles W., and Clifford W. Smith.Managing Financial Risk: A Guide to

Derivative Products, Financial Engineering, and Value Maximization. 3rd ed. Burr

Ridge, IL: Irwin McGraw-Hill, 1998.

An option is a financial instrument that gives its holder the choice of purchasing (call

option) or selling (put option) an underlying security at a predetermined price. Most

options are for limited periods, so the choice must be exercised before the option

expires.

Read more: Call and Put Options

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Options.html#ixzz1YPMh8ktU

The security on which the option is written is known as the underlying security. The

price that the option purchaser must pay to exercise the option is known as theexercise price or strike price. Strike prices are adjusted for stock splits and

dividends,but not cash dividends. The expiration date is the last date on which the

option may be exercised. An American option may be exercised at any time up to and

including the expiration date. A European option can be exercised only at the

expiration date.

An option is said to be "in-the-money" if by exercising the option it would produce a

gain. Call options are in-the-money when the market price of the underlying securityis greater than the exercise price. Put options are in-the-money when the market

price of the underlying security is less than the exercise price. Call options are said to

be "out-of-the-money" when the exercise price is more than the market price of

underlying security. Puts are out-of-the-money when the market price of the

underlying security is more than the exercise price.

The following discussion of options will use a call option as the example. Everything

stated, however, also holds for putsthe reader should keep in mind that thetransaction is reversed.
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A typical call option may be written to give its buyer the option to purchase 100

shares of the PDQ Corporation at a price of $60 per share before a stated expiration

date. The writer (i.e., seller) of the option will receive a premium for writing the

option. The per share premium is the option price divided by the number of shares inthe option. (While most premiums are quoted on a per share basis, options are

generally written for 100 shares.) The purchaser of a call option hopes that either (1)

the price of the underlying security will increase beyond the exercise price plus the

cost of the option, thereby making exercise profitable; or (2) the premium on the

option increases, thereby making sale of the option profitable.

Both buying and selling options offer profit opportunities. Buyers of call options have

the following advantages:

They know in advance the price they are going to pay (i.e., the exercise price).

They know in advance the maximum loss they can sustain on the option if they

choose not to exercise (i.e., the cost of the option).

They have the opportunity to benefit from the extreme amount of leverage

implicit in most options.

Advantages to the seller include an opportunity to increase income from theunderlying security in the option. For example, assume a portfolio contains some

stock, the price of which is drifting around a certain market price. The investor

could write an option against that stock and generate a profit, to the extent of the

premium in the option, thereby gaining even though the stock's price has not moved.

Sellers who write options against securities held in their portfolios are said to be

selling covered options. Options written without the underlying security in the

writer's portfolio are known as naked options. Writers of naked options must have

adequate funds on deposit with their broker to cover the options, should they be

exercised.

The premium related to the option is pivotal to options trading. The lower the

premium, the more favorable the option is to the purchaser for two reasons: (1) the

purchaser can hope to subsequently sell the option at a higher premium, or (2) if the

market price of the underlying security rises above the exercise price of the option,
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the purchaser can always exercise the option, thereby acquiring the security from the

option writer at below the security's current market value.

For example, assume an option for 100 shares is purchased for $200 (premium of $2

per share) while a stock is selling at $30 per share and the exercise price is $35. If the

price of the stock rises to $38, the option price should rise to at least $3 ($38 - $35),

and more likely will rise close to $5 [($38 - $35) + $2]. If the price of this option rises

to $3, the holder can either sell the option and realize a profit of $100 (a 50 percent

profit margin), or the holder can exercise the option, purchasing the shares for$3,500 instead of $3,800.

FACTORS AFFECTING OPTION PRICE

There are several factors that affect the amount of an option's premium. The

premium will be a reflection of demand and supply. During periods of rising stock

market prices, there is an increased interest in purchasing options. Conversely,

individuals owning securities would be less interested in writing options, opting to

hold their stock for further price appreciation. The combination of these two typically

raises the level of option premiums. When stock prices are declining, there is greater

interest in writing call options but less in buying them; premiums thus tend to

decline.

In addition, there are at least four other factors that interact to influence the level,

and movement, of call option premiums:

THE CURRENT MARKET PRICE OF THE STOCK.Whenever the option is in-the-money, the option price will rise if the price of the

stock continues to rise, since the option has value in addition to the time-lock

inherent in every option.

TIME.

Everything else remaining equal, the more time remaining until the option's

expiration date, the higher its premium will be. This only makes sense, since the

longer an option has to run, the less risk there is to the option holder that the exercise
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price will not rise to a level to make the option profitable. As the option approaches

its expiration date, its time value declines, and near expiration, its only value will be

the excess, if any, of the underlying security's market price over the exercise price.

It is because of the time value that it is likely an option will still have market value

even though its exercise price plus premium is below the market value of the

underlying security.

It is because of the time value that it is likely an option will still have market value

even though its exercise price plus premium is below the market value of the

underlying security.

VOLATILITY.

If the price of the underlying security fluctuates substantially, the option is likely to

command a heftier premium than an option for a security that normally trades in a

narrow price range. As a general rule, call option premiums neither increase nor

decrease point for point with the price of the underlying security. That is, a one pointincrease in the underlying security price commonly results in less than a one point

increase in the call option premium. Reasons for this include:

Rising premiums reduce the leverage inherent in the option. For example, if the

price of a stock is $100 and the option is $10, the buyer's leverage is 10:1. But if a $1

increase in the stock price were to raise the option premium by the same amount, the

leverage would be reduced.

A rise in the stock price increases the buyer's capital outlay and risk. For example,

an increase in stock price from $50 to $51 is only 2 percent, but a rise in option

premium from $5 to $6 is a 20 percent increase.

Assuming the underlying security has been in an upward trend, the option will

have less time value, decreasing its attractiveness.


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THE RISK-FREE RATE OF RETURN.

This action of the variable is not as clear. Since increasing interest rates tend to

depress stock prices, this should also cause call option prices to decrease and put

option prices to increase. On the other hand, if you choose to acquire the underlying

stock, instead of an option, the cost to finance the purchase would increase if the risk-

free interest rate increases. Therefore, the call option would be preferred over a

purchase, since the only cash outflow would be the cost of the premium.

As a result of the interaction of these variables, an in-the-money call option's price

will be at least equal to the difference between the market price and the exercise price

of the underlying security. If the underlying security's market price is near zero, it is

conceivable that the option will be worthless. Therefore, the minimum price of an

option is zero. Its maximum price will equal this difference plus the algebraic sum of

the value of the above factors, limited by the market price of the security. An out-of-

the-money call option's price will be a function of just the above factors. Note that as

the expiration date of the option nears, the effects of these other factors are

significantly diminished. The figure illustrates these relationships.

In recent years, most analysts have been using the Black-Scholes model for the

valuation of options. This model is designed for European options and is

mathematically complex. Several software packages, however, have been developed,

which makes its application considerably easier. As a result, it has gained widespread

acceptance.

BUYERS' STRATEGIES

One of the main advantages of purchasing a call option is to have a security with

mega-leverage. For example, going back to the earlier case, assume an option is

written for a stock selling at $30. The option's exercise price is $35 and the option is

selling for $2. Consider two investors with $3,000 to invest:

Investor A purchases 100 shares of stock and investor B purchases 1500

options. If the price of the stock rises to $38, the investor in the stock will have a

profit of $800 ($3,800 - $3,000), or 26.7 percent. Assuming the options rise in price
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to $3 ($38 . $35), and, it is likely the price will be higher, Investor B realizes a profit

of $1,500($4,500 - $3,000), or 50 percent.

The call option purchaser also has the benefit of limited risk. Should the price of theunderlying security decline, the option holder's maximum loss is always the price

paid for the option (i.e., his total investment in the option).

A holder of an American call option can always exercise the option before the

expiration date. This is done only when the market value of the underlying security is

above the exercise price of the option. Because the commissions to sell an option,

however, are less than the commissions to both buy and sell the underlying security,

most option holders prefer to simply sell the option rather than exercise it. Should theoption be exercised, the Options Clearing House randomly selects a member with an

outstanding short position in the same option to conclude the transaction.

Another strategy for call options, assuming the holder believes there will be a rising

market and wishes to purchase the underlying security in the future, is to lock in the

price of the underlying security. This is especially useful if the investor anticipatescash flow in the future to pay for the purchase.

A final strategy for which call options are used is to hedge against a short sale since

the option establishes the maximum price that will have to be paid for a security in

order to satisfy the obligation of a short sale.

Lastly, should an investor sell a stock at a loss, buying a call option within the 30-day

period before and after the sale would constitute a wash sale and result in the loss

being disallowed for income tax purposes.

SELLERS' STRATEGIES

Assume an owner of 100 shares of stock that cost $50 a share can write an option at a

premium of $5 per share. The stock would be deposited with the writer's broker and

his account would be credited for $500. Note that the $500 belongs to the writer


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whether or not the option is exercised. It is erroneous, therefore, to think of the

premium as a "down payment."

If the exercise price is below the market value of the security as the expiration date is

approached, option writers can reasonably assume an option will be exercised and

they will have to deliver the underlying security. Note that writers can always

terminate their obligation to deliver the security by simply purchasing an identical

option at the current premium, thereby liquidating their position.

[ Ronald M. Horwitz ]

FURTHER READING:

Brigham, Eugene F., Louis C. Gapenski, and Michael C. Ehrhardt.Financial

Management: Theory and Practice. 9th ed. Fort Worth, TX: Dryden Press, 1999.

Hull, John C. Options, Futures, and Other Derivatives. 3rd ed. Upper Saddle River,

NJ: Prentice Hall, 1997.

Kolb, Robert W. Understanding Options. New York: Wiley, 1995.

Wilson, Thomas E., and others. "Valuing Stock Options: A Cost-Effective Spreadsheet

Template." CPA Journal65, no. 3 (March 1995): 50.

financial engineering is a multidisciplinary field involving financial theory

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