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- Title
In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A partial differential equation that changed the world.
- Authors
Jarrow, Robert A.
- Abstract
This article presents an explanation of the Black-Merton-Scholes option pricing theory. To understand the Black-Merton-Scholes model, one first needs to understand what an option contract is. There are four basic types of option contracts: European calls, European puts, American calls and American puts. The key difference between the European call option and a forward contract is that for the option contract, the long does not have to buy the stock at the maturity date. For the forward contract, the long must purchase. A rational holder will, therefore, only exercise the option to purchase at the maturity date if the stock price at that time exceeds the exercise price. The original hedging argument underlying the Black-Merton-Scholes option pricing technology, although profound in implications, is quite intuitive. The idea contains three parts. Part one recognizes that a call option on the stock increases in value when the stock price rises. Part two uses an implication of this insight. Part one implies that a short position in the stock can be used to hedge against changes in the value of a call option to its holder. A short position in a stock is equivalent to holding a negative number of shares. Part three modifies the partially hedged position in the long call option and short stock to make it an exact hedge over a short time period.
- Subjects
OPTIONS (Finance); BLACK, Fischer; MERTON, Robert C.; SCHOLES, Myron S.; STOCK prices; HEDGING (Finance)
- Publication
Journal of Economic Perspectives, 1999, Vol 13, Issue 4, p229
- ISSN
0895-3309
- Publication type
Article
- DOI
10.1257/jep.13.4.229