To: dwight martin who wrote (36335 ) 2/24/1998 9:36:00 PM From: michael modeme Read Replies (2) | Respond to
In terms of the stochastic models I mentioned, they take the stock price to be a random variable, meaning that outcomes are random and drawn from some specified distribution. For example, the score that an individual gets on a test (in a classroom or otherwise) is a random variable (before we know the outcome) with a normal distribution (bell curve). This means that a randomly chosen individual in the class will his/her score drawn from a bell-shaped distribution -- more likely to get a score close to the mean, etc. Well, people who construct these models assume a certain distribution whose parameters are determined from previous stock market data. Then it is the sequence of these random variables that makes up the stochastic process describing the stock price as a function of time. For example, the simplest model takes the stock price at time t (denoted S(t) ), and then picks the next stock price at time t+1 from a distribution dependent only on the value of St. As an example of this consider the
following game: you flip a coin and win $1 if it is heads, and lose $1 if it is tails. So, each step of the process your sum either goes up $1 with probability 1/2 or goes down $1 with probability 1/2. A sample of this may look like: 0,1,2,1,0,1,2,3,4,3,4,5,4,3,2,3,...etc. So, if we could apply a simple model like this to ASND. ASND closed at $35 and change, to predict tomorrow's price we may say that ASND has a probability of p1 to go to $36, probability p2 to go to $37, p3 -> $34, etc. all of these probabilities make up the distribution. Then the next day we may change all of the probabilities based on what ASND closed at and repeat the process each day. These types of models are very very useful in predicting stock prices as well as option prices (some people get paid high six-figures for analyzing these models for brokerage houses!). So, (if you've bothered to read this far) this model is actually somewhat similar to your suggestion of an n sided die, only with differing probabilities of landing
on any one side. Hope this helps. Black and Schole won the Nobel for doing this stuff!!
