Volatility & The Black Scholes Model
Volatility and the Black-Scholes Model
Volatility
Volatility can be a very important factor in deciding what kind of options to buy or sell. Volatility shows the investor the range that a stocks price has fluctuated in a certain period. The official mathematical value of volatility is denoted as "the annualized standard deviation of a stocks daily price changes."
There are two types of Volatility: Statistical Volatility and Implied Volatility.
Statistical Volatility
A measure of actual asset price changes over a specific period of time.
Implied Volatility
A measure of how much the "market place" expects asset price to move, for an option price. That is, the volatility that the market itself is implying.
Note: The computation of volatility is a difficult problem for mathematical application.
Black-Scholes
In the Black-Scholes model, volatility is defined as the annual standard deviation of the stock price. There is a way in which the strategist can let the market compute the volatility for him.
This is called using the implied volatility - that is, the volatility that the market itself is implying. This is similar to an efficient market hypothesis. If there is enough trading interest in an option that is close to the money, that option will generally be fairly priced.
The Black-Scholes Formula
The Black-Scholes formula was the first widely-used model for option pricing. This formula can be used to calculate a theoretical value for an option using current stock prices, expected dividends, the option's strike price, expected interest rates, time to expiration and expected stock volatility.
While the Black-Scholes model does not perfectly describe real-world options markets, it is still often used in the valuation and trading of options.
The variables of the Black Scholes formula are:
- Stock Price
- Strike Price
- Time remaining until expiration expressed as a percent of a year
- Current risk-free interest rate
- Volatility measured by annual standard deviation.
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