Winners Of The 1997 Nobel Prizes In Economy

Winners Of The 1997 Nobel Prizes In Economy

Winners of​ the​ 1997 Nobel Prizes in​ Economy
The Royal Swedish Academy of​ Sciences has decided to​ award the​ Bank of​ Sweden Prize in​ Economic Sciences in​ Memory of​ Alfred Nobel 1997, to​ Professor Robert C .​
Merton, Harvard University, and​ to​ Professor Myron S .​
Scholes, Stanford University, jointly .​
The prize was awarded for​ a​ new method to​ determine the​ value of​ derivatives.
This sounds like a​ trifle achievement - but it​ is​ not .​
It touches upon the​ very heart of​ the​ science of​ Economics: the​ concept of​ Risk .​
Risk reflects the​ effect on the​ value of​ an​ asset where there is​ an​ option to​ change it​ (the value) in​ the​ future.
We could be talking about a​ physical assets or​ a​ non-tangible asset, such as​ a​ contract between two parties .​
An asset is​ also an​ investment, an​ insurance policy, a​ bank guarantee and​ any other form of​ contingent liability, corporate or​ not.
Scholes himself said that his formula is​ good for​ any situation involving a​ contract whose value depends on the​ (uncertain) future value of​ an​ asset.
The discipline of​ risk management is​ relatively old .​
As early as​ 200 years ago households and​ firms were able to​ defray their risk and​ to​ maintain a​ level of​ risk acceptable to​ them by redistributing risks towards other agents who were willing and​ able to​ assume them .​
In the​ financial markets this is​ done by using derivative securities options, futures and​ others .​
Futures and​ forwards hedge against future (potential - all risks are potentials) risks .​
These are contracts which promise a​ future delivery of​ a​ certain item at​ a​ certain price no later than a​ given date .​
Firms can thus sell their future production (agricultural produce, minerals) in​ advance at​ the​ futures market specific to​ their goods .​
The risk of​ future price movements is​ re-allocated, this way, from the​ producer or​ manufacturer to​ the​ buyer of​ the​ contract .​
Options are designed to​ hedge against one-sided risks; they represent the​ right, but not the​ obligation, to​ buy or​ sell something at​ a​ pre-determined price in​ the​ future .​
An importer that has to​ make a​ large payment in​ a​ foreign currency can suffer large losses due to​ a​ future depreciation of​ his domestic currency .​
He can avoid these losses by buying call options for​ the​ foreign currency on the​ market for​ foreign currency options (and, obviously, pay the​ correct price for​ them).
Fischer Black, Robert Merton and​ Myron Scholes developed a​ method of​ correctly pricing derivatives .​
Their work in​ the​ early 1970s proposed a​ solution to​ a​ crucial problem in​ financing theory: what is​ the​ best (=correctly or​ minimally priced) way of​ dealing with financial risk .​
It was this solution which brought about the​ rapid growth of​ markets for​ derivatives in​ the​ last two decades .​
Fischer Black died in​ August 1995, in​ his early fifties .​
Had he lived longer, he most definitely would have shared the​ Nobel Prize.
Black, Merton and​ Scholes can be applied to​ a​ number of​ economic contracts and​ decisions which can be construed as​ options .​
Any investment may provide opportunities (options) to​ expand into new markets in​ the​ future .​
Their methodology can be used to​ value things as​ diverse as​ investments, insurance policies and​ guarantees.
Valuing Financial Options
One of​ the​ earliest efforts to​ determine the​ value of​ stock options was made by Louis Bachelier in​ his Ph.D .​
thesis at​ the​ Sorbonne in​ 1900 .​
His formula was based on unrealistic assumptions such as​ a​ zero interest rate and​ negative share prices.
Still, scholars like Case Sprenkle, James Boness and​ Paul Samuelson used his formula .​
They introduced several now universally accepted assumptions: that stock prices are normally distributed (which guarantees that share prices are positive), a​ non-zero (negative or​ positive) interest rate, the​ risk aversion of​ investors, the​ existence of​ a​ risk premium (on top of​ the​ risk-free interest rate) .​
In 1964, Boness came up with a​ formula which was very similar to​ the​ Black-Scholes formula .​
Yet, it​ still incorporated compensation for​ the​ risk associated with a​ stock through an​ unknown interest rate.
Prior to​ 1973, people discounted (capitalized) the​ expected value of​ a​ stock option at​ expiration .​
They used arbitrary risk premiums in​ the​ discounting process .​
The risk premium represented the​ volatility of​ the​ underlying stock.
In other words, it​ represented the​ chances to​ find the​ price of​ the​ stock within a​ given range of​ prices on expiration .​
It did not represent the​ investors' risk aversion, something which is​ impossible to​ observe in​ reality.
The Black and​ Scholes Formula
The revolution brought about by Merton, Black and​ Scholes was recognizing that it​ is​ not necessary to​ use any risk premium when valuing an​ option because it​ is​ already included in​ the​ price of​ the​ stock .​
In 1973 Fischer Black and​ Myron S .​
Scholes published the​ famous option pricing Black and​ Scholes formula .​
Merton extended it​ in​ 1973.
The idea was simple: a​ formula for​ option valuation should determine exactly how the​ value of​ the​ option depends on the​ current share price (professionally called the​ delta of​ the​ option) .​
a​ delta of​ 1 means that a​ $1 increase or​ decrease in​ the​ price of​ the​ share is​ translated to​ a​ $1 identical movement in​ the​ price of​ the​ option.
An investor that holds the​ share and​ wants to​ protect himself against the​ changes in​ its price can eliminate the​ risk by selling (writing) options as​ the​ number of​ shares he owns .​
If the​ share price increases, the​ investor will make a​ profit on the​ shares which will be identical to​ the​ losses on the​ options .​
The seller of​ an​ option incurs losses when the​ share price goes up, because he has to​ pay money to​ the​ people who bought it​ or​ give to​ them the​ shares at​ a​ price that is​ lower than the​ market price - the​ strike price of​ the​ option .​
The reverse is​ true for​ decreases in​ the​ share price .​
Yet, the​ money received by the​ investor from the​ buyers of​ the​ options that he sold is​ invested .​
Altogether, the​ investor should receive a​ yield equivalent to​ the​ yield on risk free investments (for instance, treasury bills).
Changes in​ the​ share price and​ drawing nearer to​ the​ maturity (expiration) date of​ the​ option changes the​ delta of​ the​ option .​
The investor has to​ change the​ portfolio of​ his investments (shares, sold options and​ the​ money received from the​ option buyers) to​ account for​ this changing delta.
This is​ the​ first unrealistic assumption of​ Black, Merton and​ Scholes: that the​ investor can trade continuously without any transaction costs (though others amended the​ formula later).
According to​ their formula, the​ value of​ a​ call option is​ given by the​ difference between the​ expected share price and​ the​ expected cost if​ the​ option is​ exercised .​
The value of​ the​ option is​ higher, the​ higher the​ current share price, the​ higher the​ volatility of​ the​ share price (as measured by its standard deviation), the​ higher the​ risk-free interest rate, the​ longer the​ time to​ maturity, the​ lower the​ strike price, and​ the​ higher the​ probability that the​ option will be exercised.
All the​ parameters in​ the​ equation are observable except the​ volatility , which has to​ be estimated from market data .​
If the​ price of​ the​ call option is​ known, the​ formula can be used to​ solve for​ the​ market's estimate of​ the​ share volatility.
Merton contributed to​ this revolutionary thinking by saying that to​ evaluate stock options, the​ market does not need to​ be in​ equilibrium .​
It is​ sufficient that no arbitrage opportunities will arise (namely, that the​ market will price the​ share and​ the​ option correctly) .​
So, Merton was not afraid to​ include a​ fluctuating (stochastic) interest rate in​ HIS treatment of​ the​ Black and​ Scholes formula.
His much more flexible approach also fitted more complex types of​ options (known as​ synthetic options - created by buying or​ selling two unrelated securities).
Theory and​ Practice
The Nobel laureates succeeded to​ solve a​ problem more than 70 years old.
But their contribution had both theoretical and​ practical importance .​
It assisted in​ solving many economic problems, to​ price derivatives and​ to​ valuation in​ other areas .​
Their method has been used to​ determine the​ value of​ currency options, interest rate options, options on futures, and​ so on.
Today, we no longer use the​ original formula .​
The interest rate in​ modern theories is​ stochastic, the​ volatility of​ the​ share price varies stochastically over time, prices develop in​ jumps, transaction costs are taken into account and​ prices can be controlled (e.g .​
currencies are restricted to​ move inside bands in​ many countries).
Specific Applications of​ the​ Formula: Corporate Liabilities
A share can be thought of​ as​ an​ option on the​ firm .​
If the​ value of​ the​ firm is​ lower than the​ value of​ its maturing debt, the​ shareholders have the​ right, but not the​ obligation, to​ repay the​ loans .​
We can, therefore, use the​ Black and​ Scholes to​ value shares, even when are not traded .​
Shares are liabilities of​ the​ firm and​ all other liabilities can be treated the​ same way.
In financial contract theory the​ methodology has been used to​ design optimal financial contracts, taking into account various aspects of​ bankruptcy law.
Investment evaluation Flexibility is​ a​ key factor in​ a​ successful choice between investments .​
Let us take a​ surprising example: equipment differs in​ its flexibility - some equipment can be deactivated and​ reactivated at​ will (as the​ market price of​ the​ product fluctuates), uses different sources of​ energy with varying relative prices (example: the​ relative prices of​ oil versus electricity), etc .​
This kind of​ equipment is​ really an​ option: to​ operate or​ to​ shut down, to​ use oil or​ electricity).
The Black and​ Scholes formula could help make the​ right decision.
Guarantees and​ Insurance Contracts
Insurance policies and​ financial (and non financial) guarantees can be evaluated using option-pricing theory .​
Insurance against the​ non-payment of​ a​ debt security is​ equivalent to​ a​ put option on the​ debt security with a​ strike price that is​ equal to​ the​ nominal value of​ the​ security .​
a​ real put option would provide its holder with the​ right to​ sell the​ debt security if​ its value declines below the​ strike price.
Put differently, the​ put option owner has the​ possibility to​ limit his losses.
Option contracts are, indeed, a​ kind of​ insurance contracts and​ the​ two markets are competing.
Complete Markets
Merton (1977) extend the​ dynamic theory of​ financial markets .​
In the​ 1950s, Kenneth Arrow and​ Gerard Debreu (both Nobel Prize winners) demonstrated that individuals, households and​ firms can abolish their risk: if​ there exist as​ many independent securities as​ there are future states of​ the​ world (a quite large number) .​
Merton proved that far fewer financial instruments are sufficient to​ eliminate risk, even when the​ number of​ future states is​ very large.
Practical Importance
Option contracts began to​ be traded on the​ Chicago Board Options Exchange (CBOE) in​ April 1973, one month before the​ formula was published.
It was only in​ 1975 that traders had begu​n applying it​ - using programmed calculators .​
Thousands of​ traders and​ investors use the​ formula daily in​ markets throughout the​ world .​
In many countries, it​ is​ mandatory by law to​ use the​ formula to​ price stock warrants and​ options .​
In Israel, the​ formula must be included and​ explained in​ every public offering prospectus.
Today, we cannot conceive of​ the​ financial world without the​ formula.
Investment portfolio managers use put options to​ hedge against a​ decline in​ share prices .​
Companies use derivative instruments to​ fight currency, interest rates and​ other financial risks .​
Banks and​ other financial institutions use it​ to​ price (even to​ characterize) new products, offer customized financial solutions and​ instruments to​ their clients and​ to​ minimize their own risks.
Some Other Scientific Contributions
The work of​ Merton and​ Scholes was not confined to​ inventing the​ formula.
Merton analysed individual consumption and​ investment decisions in​ continuous time .​
He generalized an​ important asset pricing model called the​ CAPM and​ gave it​ a​ dynamic form .​
He applied option pricing formulas in​ different fields.
He is​ most known for​ deriving a​ formula which allows stock price movements to​ be discontinuous.
Scholes studied the​ effect of​ dividends on share prices and​ estimated the​ risks associated with the​ share which are not specific to​ it .​
He is​ a​ great guru of​ the​ efficient marketplace (The Invisible Hand of​ the​ Market).

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