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. 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.
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