Black Scholes Model
by admin on 19/07/09 at 12:07 pm
Today’s financial analysts have developed their techniques that enable them to calculate, with alarming accuracy, the value of a stock option. Most of the models and techniques employed originate from a model developed by Fischer Black and Myron Scholes in 1973.
The Black–Scholes model is a mathematical model of the market for an equity, in which the equity’s price is a stochastic process. The model makes the following assumptions:
- It is possible to borrow and lend cash at a known constant risk-free interest rate.
- The price of the equity follows a geometric Brownian motion with constant drift and volatility.
- Transactions made incur no costs
- The stock does not pay a dividend.
- All securities are perfectly divisible (i.e. it is possible to buy any fraction of a share).
- There are no restrictions on short selling.
From these ideal conditions in the market for an equity (and for an option on the equity), the authors show that “it is possible to create a hedged position, consisting of a long position in the stock and a short position in [calls on the same stock], whose value will not depend on the price of the stock.”
