Evaluation of the expected future price, expected future variance of the price, probability associated with a given future price range, and future price range associated with a given probability in accordance with the Black-Scholes model.
For a list of all members of this type, see PriceRange Members.
System.Object
PriceRange
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.
Namespace: WebCab.COM.Finance.Options
Assembly: WebCab.COM.Options (in WebCab.COM.Options.dll)
PriceRange Members | WebCab.COM.Finance.Options Namespace | PriceRangeStateful - Offers the same functionality as this class within a stateful class.