Challenge
Hidden potentia
To solve signals dilemma, we introduce challenge - it is closely related to underlying model of exchange rate as a Brownian motion.
The picture below provides good visual example how exchange rate can develop from a given starting point. Few comments:
majority of trajectories are around 'zero point' - that is the starting point
the larger distance from 'zero point' the lower probability that the exchange rate will hit this level
overall trajectories are well described by square root time-deviation curve. This is precisely what assumes model of Brownian motion with static parameters:
Brownian motion deviation ( t ) = [ constant deviation ] * [ square root ( t ) ].
IQUO uses arithmetic version of Brownian motion with zero drift. The choice is made under assumptions of high liquidity of predicted currencies and short term nature of predictions, - which effectively excludes a possibility of critical exchange rate changes. Arithmetic Brownian motion is also more gas efficient on contracts side.
Based on the above, we can build a series of parabolas to denote areas of different 'challenge' of prediction - the larger the distance of a prediction point from 'zero point' the lower the probability of respective outcome and respectively the higher associated value of 'challenge'. At the same time we assume the 'challenge' to be constant along every parabola:
It turns out that we can directly apply this logic to signals - let us look at this:
Here we have signals 1, 2 and 8 to have equally high 'challenge', while signals 3, 4, 5, 6, 7 do have a lower but also constant 'challenge'. Let us formalise 'challenge' and introduce it as a signal parameter:
challenge = [ distance ] / { square root (( [ expiration time ] - [ creation time ] ) / [ benchmark timespan ] ) }, or
challenge = [ distance ] / { square root ( [ duration ] / [ benchmark timespan ] ) } :
(now we can use the word 'challenge' without apostrophes, as a model parameter).
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