patteren:
042707;117 
the simplest form of options pricing involves a decision tree which maps possible outcomes at succeeding points in time : probabilities are assigned to each possible outcome, and the value of the option is determined by the likelihood of each outcome at the time of the option's expiration : the value will depend on several factors, including the number of periods, or time, and the volatility, or how far the price moves for each node on the decision tree : in effect, this method reduces all possible future outcomes, or choices, to the present moment using the statistical likelihood of each possible future choice : the underlying, or spot market price, will have an actual value as time progresses, but for the present moment, the options price is the single value of all future movements of the underlying : so options pricing is a map of future movements : it is equivalent to pythagoras' map of the future movements of harmony based on the overtone series : these maps are derivatives of the underlying that are environments unto themselves : that is, the option is a market unto itself, traded as an underlying as is the underlying spot commodity : it is circular, that is, options can be the underlying for further derivatives, options on options : similarly, pythagoras' map is circular, his overtone series divided the octave into 12 increments which created the scale and it is the evolution of the use of the scale that fulfilled the prophecy of the tonal map 
