options - chapter 1

7/31/2019 Options - Chapter 1

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Chapter 1

Introduction to Financial Derivatives

Ill fares the land, to hastning ills a prey,Where wealth accumulates, and men decay.

OLIVER GOLDSMITH, The Deserted Village (1770)

Wealth is not without its advantages, and the case to the contrary, although it has often been made, has neverproved widely persuasive.

JOHN KENNETH GALBRAITH, The Affluent Society (1958)

Finance is about wealthaccumulating and preserving it. The effect of wealth on the lives of

even the least avaricious man is enormous. When men decay in accumulating wealth, history proved

Goldsmith right: look no further than the fall of Venice, Florence, Holland, and England as centers of

international finance.

1.1. Wealth

Before civilization, wealth was necessary: it meant the basic necessities ( ie, food, clothing and

shelter) that were hunted. Civilization brought in the concepts of family, progeny and leisure. Man had to

hunt and hoard wealth because it was required for next days consumption, for next generationsconsumption. What had been a need became greed, too.

Now and then there was an odd man, like Prince Siddhartha, who preached that wealth (andeverything else) was misery. The great majority, however, thought that hoarding wealth was not misery

but a virtue worthy of effort. Though philosophers, theologians and aristocrats did spurn wealth, they still

had self-interest in it. Philosophers were a leisured class; theologians were propped up by the charity ofthe wealthy; and aristocrats were what they were because of their wealth. Wealth was even justified by a

new branch of science called economics, which inquired into wealth. Assured thus that wealth is not acrime, vice or sin, we will proceed further to study it.

1.2. Physical Assets

Hoarding wealth required storing it. The medium for storing wealth was different in different

waves of civilization. In the first wave, marked by agriculture, wealth was stored in physical assets such

as land, house and precious metals. Physical assets had visibility, which assured one of ones wealth.They had solidity, too, giving the possessor a feeling of permanence. Their disadvantage was that they

were cumbersome for exchange and prone to loss from natural calamities or theft. Besides, they put a

limit on the expansion of wealth. The situation led to the invention offiduciaryassets.

1.3. Fiduciary Assets

Fiduciary assets were paper money. Whereas physical assets required none else, fiduciary

assets required two counterparts to store wealth: the issuer and the holder. It made wealth a financial

contract or claim between two counterparts.

Fiduciary assets were handy to store, exchange, and transport wealth. They were not subject to

risk from natural calamities and theft. More important, they were self-growing: wealth could earn interest


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on its own, which was the second conceptual breakthrough with fiduciary assets. The following passage

from John Galsworthys novel, The Man of Property, aptly captures the attitude to wealth.

Why dont you go into country? repeated June; it would do you a lot of good.

Why? began James in a fluster. Buying landwhat good dyou suppose I can do buying land, building

houses?I couldnt get four per cent. for my money!

What does that matter? Youd get fresh air.

Fresh air! exclaimed JamesYou dont know the value of money, he said, avoiding her eye. Fiduciary assets took different forms. There was paper money issued by central banker, who was

more honorable than others. There were IOUs between counterparts who were slightly less honorable,

though not so less as to be dishonorable.

The danger from fiduciary assets was the failure of the issuer to perform the promise. There were

occasional problems between a Shylock and an Antonio. However, the system of wealth had always a

Portia around to intelligently solve the problem. The problems sprang up more out of greed than dishonor.

The contract was held so sacred a covenant that the system of wealth was safe.

In the second wave of civilization, which brought in industrialization, someone invented a new

class of assets, shares and stocks, which offered higher return than other fiduciary assets. The higherreturn, however, demanded two concessions. First, the higher return was an expectation, not a promise.

Second, the contract had indefinite life. The former was tolerable: the latter was not. This led to the birthof the secondarymarketwhere wealth could be traded by the wealthy.

Over time, honesty fell and greed rose among the wealth-seekers. Holland, which was the center

of international finance during the 17th

century, suffered the Tulip Mania in 1630s. England, which took

over the mantle from Holland during the 18th

century, had similar crisis in the South Sea Bubble in 1720.

The stocks and shares gave their holders high return and, of course, higher risk. It appeared as if the risk

were the original sin and the return was born with it. For, there is no return without commensurate risk.

Despite an occasional mania or crisis, fiduciary assets stuck as the predominant medium for

wealth, and were collectively calledfinancial assets. Bonds and other fixed-income assets had guaranteed

return, and were called risk-free assets1. Stocks and shares, which had no such guarantee for return, were

called risky assets.

1.4. Derivative Assets

The third wave of civilization, which is the present postindustrial society, invented yet another

medium for wealth: derivative assets. Derivative assets are so called because they derive their existence

from that of another called the underlying asset. Without the underlying asset, the derivative asset does

not exist.

For example, the stock of State Bank of India (SBI) is the underlying asset. A contract today to

buy or sell SBI stock for delivery and settlement on a later day is a derivative asset: it is called a forward

or futures contract. The value of the derivative asset depends on the value of the underlying asset on

delivery date. History has recorded that the derivative assets had been in existence for long. However,

they became established in an organized way and scale only in the postindustrial society.Forward contract is the first derivative asset. It traces its origin to the plains of Lombard during

the 12th

century. Merchants from different countries would trade their goods in the cross-border fairs.Italian moneychangers, sitting separately on benches2, would provide foreign exchange for merchants.

1Any financial asset has credit risk (ie, default risk), which is ignored here. Risk-free asset in this book is the one with fixed

return.2Italian word for bench is banca, which is the root word for bankin many European languages. Thus, a bank is merely a bench

to sit on!


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Legend has it that the moneychanger once explained to a merchant that franc was then costly because

there was good demand for French wine. During the next fair, the merchant had gone to the

moneychanger to buy francs before the fair commenced. The moneychanger again explained to the

merchant that it was not necessary to buy franc in advance. Instead, he could commit to buy on a later

date at a rate fixed today. And that was the first forward contract. Forward contract removes the

uncertainty about the price in future. It also provides leverage: ability to buy without fully paying for it;

or sell without owning or possessing it.

Its disadvantage is that it is a private contract between two counterparts. The price contracted may

not be the market price. Nor does the market know about the price contracted. Further, if the merchant in

the example above decides not to buy French wine, he will have to cancel the forward contract with the

same counterpart and with the same lack of transparency in price. Had he bought francs in cash instead,

he could have sold it to anyone in the market. There being no secondary market for forward contract, we

may say that forward contract removes price risk but creates liquidity risk. The next derivative asset, the

futures3

contract, addressed the twin problems of price transparency and liquidity.

Futures contract is the first publicly traded derivative asset. Buyers and sellers assemble at oneplace and openly transact business in buying and selling of the underlying asset for delivery on a future

date. An initial purchase (or sale) contract entered into with a counterpart can be unwound by a reversing

sale (or purchase) with any other. Such offsetting, which enables secondary market and provides liquidity,requires some common standards for the fungibility of futures contract. Accordingly, the futures contract

is standardized for amount and delivery dates.

3We usefuture (singular) when referring to time, and futures (plural) when referring to the derivative asset. Thus, future price

means the price that will prevail on a later date; and futures price, the currentprice of the futures contract.


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Though the futures contract provides price transparency and liquidity, it also takes away

something. First, the standardization may result in imperfect hedge. For example, if the quantity of

exposure to be hedged is 102 and the market lot is 100, the hedge is complete only for 100. Further, if the

exposure is due in 31 days and the delivery of futures contract is 30 days, the exposure remains unhedged

on the 31st day. Because of standardization, the futures contract converts price risk into basis risk, which

is not as risky as price risk.

Second, futures contract has margining and mark-to-market provisions, which are safeguards

against credit risk. In the mark-to-market process, the futures price is made to reflect the current market

conditions. The change in value between the contract rate and the current rate is settled everyday between

buyer and seller. In other words, the value is made zero everyday by changing the price. In contrast, the

forward contracts price remains constant and its value changes everyday based on the current marketconditions; and the accumulated change in value is settled at maturity. Overall, the futures contract gives

more than what it takes away, and has become more popular than forward contracts.

There are many kinds of derivative assets: forwards, futures, options, swaps, asset-backed

securities, structured notes, and credit derivatives. Broadly, the sequence in the list is also the sequence of

their appearance in markets. This book analyzes the option instrument in detail, and a brief comment on

other derivatives is given below.

Asset-backed securities rolled out from the securitization of mortgages in the USA. Theunderlying mortgage security is split into interest-only (IO) and principal-only (PO) strips, and traded

separately in the market. Alternatively, a 6% mortgage with a face value of 100 may be split into a

discount strip of 2% bond with a face value of 50 and a premium strip of 10% bond with a face value of

50. These derivative assets behave like fixed-income securities with unusual properties (ie, negative

convexity, negative duration) because of prepayment feature. A particular investor may indeed desiresuch unusual features given a particular outlook on interest rate changes or particular risk-return profile.

Structured notes are bonds whose yield is linked to a reference yield or the market price of an

asset in a specified way. For example, inverse floater is a floating-rate security that pays lesser interest as

the reference market rate (such as LIBOR) goes up. Though it appears unusual or even irrational, the

inverse floater gains in value when the interest rate falls. Range floater is a combination of simplefloating-rate security with a ceiling and floor for the rate. Other structured notes include bonds that pay

interest rate according to the level of market price of a specified commodity or stock index. Some such as

dual currency bonds pay interest in a foreign currency.

Credit derivatives are the latest derivatives and have appeared in the 1990s. They separate credit

risk from interest rate risk in a fixed-income security, and trade the former. Credit risk is perhaps the

oldest risk known in banking industry and yet assessed subjectively and differently by bankers. The price


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of a traded credit derivative is the price of credit risk perceived by the market, which may be a better

indicator than that assessed by a particular banker.

It is important to recognize that the common element among all derivative assets is that they

derive their existence from that of an underlying asset. Thus, the cross rates in foreign exchange such asGBP/DEM or DEM/INR can be considered derivatives because they derive their existence from two

underlying assets that are quoted against the numeraire USD.Derivatives are often confused with off-balance-sheet items or with those providing leverage.

Asset-backed securities and structured notes are not off-balance-sheet items and do not provide leverage.

Nor do all off-balance-sheet items qualify to be derivatives. For example, bank guarantee and letter-of-

credit are off-balance-sheet items but not derivative assets.

The pricing of derivatives is, surprisingly, easy and objective in most cases. Since the price of

derivative asset is contingent on the price of underlying asset, we can objec tively fix the fair price ofderivative asset. We need to know only the current price of the underlying asset, time-value of money,

and linkages in cashflowsnone of them is difficult or subjective. The exception to this pricing principle

is the pricing of long-dated interest rate swaps and credit derivatives. In these cases, some element of

subjectivity is apparent.

1.5. Option Contract

The need for option contract stems from the dangers of leverage in forward and futures contract.

Leverage is both an advantage and a disadvantage.

For hedging purpose, it is an advantage because it does not lead to any cash outflow at the time of

contract. For speculation, however, it is a double-edged knife. With a leverage of 10, a gain of one

percent in the price of underlying asset will translate into a gain of 10 percent. The same magnification

applies to loss, too. At higher levels of leverage, the risk will be so high and dangerous that it may

overshadow the return and prompt the holder to back out of the contract. The backing out, however, is

against the covenant. To let the higher risk coexist with higher return and yet safeguard the financial

system, the backing out is provided in the contract itself so that it was honorable. And thus was born the

option contract.

Obviously, only one counterpart can possess this privilege4

of backing out. If both were to

possess it, there would be no contract. The counterpart holding it is the holder; and the other who granted

it, the grantoror writer. In other words, the holder buys the privilege and is the option buyer; and thewriter sells the privilege and is the option seller.

The word option seller is a little confusing, and may not be precise. For example, one can sellsomething when one possesses or produces it. The option seller does neither. More important, the option

seller is selling a right on the asset, not the asset itself. The right can be as follows.

(1) Right to buy the asset, which obliges the option seller to sell the asset. In this case, hewould be selling the asset.

(2) Right to sell the asset, which obliges the option seller to buy the asset. In this case, hewould be buying the asset.

Thus, the option seller sells the right-to-buy or right-to-sell the underlying asset. We can say that

he underwrites the risk from the underlying asset; and is accordingly called the option writer.

4Options were originally called privileges. The name option was coined later.


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Any buyer has to pay for what is bought no matter whether it is an asset or a right. Therefore, the

option buyer pays the option writer the option price to secure the right-without-obligation. The loss to the

buyer is always limited: he does not lose more than the option price. The option writer, on the otherhand, is exposed to an unknown amount of loss, which could be higher than the option price. The option

contract thus appears quite unfair to the option writer and very favorable to the option buyer. We will see

in later chapters that the option price is fair to both the counterparts.

1.6. Options: Distinctive Features and Ubiquity

The option is distinct among the derivatives, and its hallmark is the right-without-obligation for

its buyer and obligation-without-right for its writer. Another feature is that it loses a part or whole of itsvalue over time; and is accordingly called a wasting asset (see sections 3.1.2.2 and 3.2.5). The other

financial assets either grow (eg, riskless assets) or expected to grow (eg, risky assets) in value as time

passes.

Strange as it may seem, the option contract is ubiquitous despite being apparently unusual. Not

only do various financial instruments but also financial activities have the option feature. In recent years,

the option theory has been generalized and applied to corporate finance. The options pricing is used to

value real options such as expenditure on R&D, advertisement, expansion, etc.

Structure of this Book

This and the next chapter are the Part I of the book. The next chapter introduces the basic option

vocabulary, and compares the option with other financial instruments.

Part II in three chapters examines the optionprice. With intuition and without mathematics, we

will analyze the nature and components in option price, and the limits on and relationship among prices of

various options.

Part III with seven chapters introduces optionpricing andhedging. It is the part that involves

mathematics. Chapter 6 describes the model for stock price changes. Stocks are the most popular financial

assets. Accordingly, options on stocks are the most popular options. The option being a contingent claim,its price would depend on the price of the underlying stock. It is necessary, therefore, to discuss the model

for stock price behavior. Chapter 7 is a primer on pricing and an essential reading. It introduces, without

mathematics, three crucial concepts in option pricing, namely, risk-free hedge portfolio, equivalent

portfolio and risk-neutral valuation. The first shows that two risky assets, when appropriately combined,

will form a risk-free portfolio. One risky asset acts as a hedge against the other, like basic principle of

like cureslike in homeopathy. This is a breakthrough, and the clue to the successful pricing of options.The second concept shows that option can be replicated by buying an appropriate quantity of underlying

asset with borrowed money, or short-selling an appropriate quantity and investing the short-sale proceeds.

Thus, even if the regulators ban options, the investors can still replicate their payoffs. The third concept is

a trick to simplify the solution to a complex mathematical equation.

Chapter 8 is the path-breaking work of Fischer Black and Myron Scholes on option pricing.Unfortunately, it is also the chapter that involves stochastic calculus, which is thepans asinorum of math-

haters. It should be noted that price is different from pricing. It is not necessary to master stochastic

calculus to use options inasmuch as it is not necessary to master automobile engineering to drive a car.

The sections with complex mathematics or statistics marked MATH or STATISTICS. Readers may safely skip

them. After all, the art of reading is to skip judiciously. (P.G. Hamerton)

Chapters 9 and 10 examine the more important side of option pricing: hedging. Replicating

options by buying and selling an appropriate quantity of underlying asset is illustrated. Chapter 11 details


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the binomial method of option pricing, which is intuitive and without mathematics, and Chapter 12 details

the other pricing models.

Part IV is the most practical part: use of options. Chapter 13 analyzes the risk and return from

options in a proper perspective using the modern portfolio theory. Chapter 14 discusses the basic option

gear required for using options. Chapters 15, 16 and 17 analyze the various option exposures for

speculation, investment and insurance, and how to select an exposure for bullish, bearish, sideways,uncertain, and volatile markets. Chapter 18 deals with portfolio insurance, a concept that has gainedsome notoriety in the wake of US stock market crash in October 1987. Chapter 19 deals with two topics:

accounting and tax treatment. For many, the former is boredom and the latter, a curse. Whether we like it

or not, the regulators require us to follow both.

Part V deals with the options market. Chapter 20 examines the structure, functioning, and

practices of organized option markets. Chapter 21 reviews the approaches to market-making in options.

Part VI is the last part of the book with three chapters. Chapter 22 generalizes the option theory to price

corporate liabilities like bonds, stocks, convertible bonds, and other instruments in corporate finance. The

last chapter reviews exotic options and the field of financial engineering.

options - chapter 1

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