Partial-recovery interval for the event clock

Under exact recovery the measured state-price log-odds quadratic variation is the physical event clock. Under the partial-recovery bound of the working paper — valuation-wedge quadratic variation no larger than \(\varepsilon^2\) times the physical clock — the sharp implied interval for the clock is $$\big((1-\varepsilon)_+\big)^2\,\widehat{A} \;\le\; A \;\le\; (1+\varepsilon)^2\,\widehat{A},$$ where \(\widehat{A}\) is the measured log-odds variation. Exact recovery is \(\varepsilon = 0\).

Usage

ec_recovery_set(A, eps = c(0, 0.1, 0.25, 0.5))

Arguments

A

Measured log-odds quadratic variation (e.g. the A column of event_clock()).

eps

Partial-recovery bound(s) \(\varepsilon \ge 0\); the default reproduces the working paper's sensitivity grid.

Value

A tibble with columns A, eps, lower, upper (one row per A \(\times\) eps combination).

Examples

ec_recovery_set(0.511)                   # Brexit 1M clock
#> # A tibble: 4 × 4
#>       A   eps lower upper
#>   <dbl> <dbl> <dbl> <dbl>
#> 1 0.511  0    0.511 0.511
#> 2 0.511  0.1  0.414 0.618
#> 3 0.511  0.25 0.287 0.798
#> 4 0.511  0.5  0.128 1.15 
ec_recovery_set(c(0.064, 0.166), eps = 0.25)
#> # A tibble: 2 × 4
#>       A   eps  lower upper
#>   <dbl> <dbl>  <dbl> <dbl>
#> 1 0.064  0.25 0.036  0.1  
#> 2 0.166  0.25 0.0934 0.259