PriceRangeStateful.VarianceOfPrice Method

Evaluates the variance of the price distribution in accordance with the Black-Scholes model at some given future point in time.

public double VarianceOfPrice();

Return Value

The expected variance (in decimal format) of the price distribution in accordance with the Black-Scholes model at a given future point in time.

Remarks

Note that the expected (future) volatility in accordance with the Black-Scholes model at the point considered is just the square root of the variance.

Pre-requisites

Before this method is called you must have set the following:

Initial Price - the initial price of the asset for which the future expected price is being evaluated which is set using SetInitialPrice.
Expected Return - the annual expected return of the asset given in decimal format (i.e. 1 percent = 0.01) which is set using either SetExpectedReturn, or one of the methods SetPriceValuesDates, SetPriceValues which uses line regression of historical price data in order to estimate the expected return.
Volatility - the (historical) volatility of the asset price per year given in decimal format (i.e. 1 percent = 0.01) which is set using SetVolatility.
Time - the time in years from the initial point in time when the initial price in measured until the expected price is evaluated which is set using SetTime(double), or SetTime(Date, Date).

Worked Example

Problem Considered

What is the variance of the price distribution of a stock in one year in accordance with the Black-Scholes model when the initial price on 4th January 2006, of the stock is 20 dollars, the expected return is 20 percent per year, with a volatility of 40 percent per year?

Parameters required to be set in order to solve this problem

initialPrice = 20
expectedReturn = 0.20
volatility = 0.40
startDate = 4/1/2006
endDate = 4/1/2007

Answer Found

By calling this method using the above parameters you will find that the variance of the price distribution of the asset on 4th January 2007, considered in accordance with the Black-Scholes model is: 103.5391. Moreover, the expected volatility of the stock in one year in accordance with the Black-Scholes model is: (103.5391)^0.5 = 10.18 percent per year.