Exact probability that the resolution-date event probability exceeds a
threshold, \(P(q_T > x)\), under the logistic-normal transition law:
$$P(q_T > x) = q\,\Phi\!\left(\frac{L + A/2 - \mathrm{logit}\,x}
{\sqrt A}\right) + (1-q)\,\Phi\!\left(\frac{L - A/2 -
\mathrm{logit}\,x}{\sqrt A}\right).$$
Arguments
- x
Numeric vector of thresholds in \((0,1)\).
- q
Numeric vector of current event probabilities in \((0,1)\).
- A
Numeric vector of event-clock time (non-negative).
Value
Numeric vector of probabilities.
Examples
# probability that the market ends up above 50% by resolution
ec_exceedance(0.5, q = 0.195, A = 0.166)
#> [1] 0.0001951016
