PriceRangeStateful.GetPriceRange Method

Evaluates the expected future price range in accordance with the Black-Scholes model to a given probability.

public double[] GetPriceRange();

Return Value

An array of length two where the first element is the lower bound of the price range and the second elements is the upper bound of the price range.

Remarks

That is, we evaluate the expected price range which an asset is expected the lie to a given probability at a future time in accordance with the Black-Scholes Model.

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 range associated to a given probability is being evaluated which is set using SetInitialPrice.
Probability - the probability in decimal format (i.e. 1 percent = 0.01) that the asset will lie within the returned price range at the future point in time in accordance with the Black-Scholes model which is set using SetProbability.
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 price range is evaluated which is set using SetTime(double), or SetTime(Date, Date).

Worked Example

Problem Considered

What is the price range of a stock in six month time to a 95 percent probability in accordance with the Black-Scholes model, when the present price of the stock on 4th January 2006, is 40 dollars, the expected return is 16 percent per year, with a volatility of 20 percent per year?

Parameters required to be set in order solve this problem

initialPrice = 40, set using SetInitialPrice.
probability = 0.95, set using SetProbability.
expectedReturn = 0.16, set using SetExpectedReturn.
volatility = 0.20, set using SetVolatility.
startDate = 4/1/2006, set using SetTime(Date, Date).
endDate = 3/7/2006, set using SetTime(Date, Date).

Answer Found

By calling this method using the above parameters you will find that the price range of the asset at the opening on 4th July 2006, to a probability of 95 percent in accordance with the Black-Scholes model is: [32.5138, 56.6048]. That is, there is a 95 percent probability that the stock considered price will be greater (or equal to) 32.5138, and less than (or equal to) 56.6048, at the opening in the 4th July 2006.