PriceRangeStateful Class

Evaluation of the expected future price, expected future variance of the price, probability associated with a given price range, and the price range associated with a given probability in accordance with the Black-Scholes model.

For a list of all members of this type, see PriceRangeStateful Members.

System.Object
   PriceRangeStateful

Remarks

Details

Here we assume that the evolution of the asset evolves in accordance with the Black-Scholes model. The key assumption of the Black-Scholes model is that the asset evolves in accordance with a geometric Brownian motion, namely:

dS(t) = drift.S(t).dt + vol.S(t).dW(t),

where S(t) is the price of the underlying asset at time t, drift is a constant rate of drift, vol is the volatility on the asset and dW(t) is a random variable associated with the normal distribution. Hence, the stock price is distributed in accordance with the Normal distribution.

Now since we know that the expected stock prices are distributed in accordance within the Normal distribution we are able to evaluate the associated probability to a range of asset prices at some future point in time when the present asset price and Black-Scholes model parameters are known. Conversely for a given future price range we are able to evaluate the probability of an assets falling within this range when the present price and the Black-Scholes model parameters are known. Finally, since the Normal probability distribution in symmetric about its mean we are able to evaluate the expected price given in the initial price and drift rate.

User Guide

This XML Web service is stateful in which the various Black-Scholes model parameters and parameters describing the asset being considered will need to be set before the main business methods can be called. In order to use the functionality contained within this XML Web service we suggest you select one of the main business methods listed below and set each of the parameters detailed within the pre-requisites. The main business methods are:

1. RangeProbability() - Evaluates the probability of the asset considered lying within the future price range in accordance with the Black-Scholes model.
2. ExpectedPrice() - Evaluates the future expected price of an asset modeled in accordance with the Black-Scholes model.
3. VarianceOfPrice() - Evaluates the variance of the price distribution in accordance with the Black-Scholes model at some given future point in time.
4. GetPriceRange() - Evaluates the expected future price range in accordance with the Black-Scholes model. 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.

Requirements

Namespace: Options

Assembly: WebCab.Options (in WebCab.Options.dll)

See Also

PriceRangeStateful Members | Options Namespace | PriceRangeStateless