Convert a call-equivalent delta grid to log-moneyness

Standardized option surfaces are usually quoted on a delta grid. Under the Black model with unit forward and total dispersion s, the strike with (call) delta \(\Delta\) has log-forward moneyness $$k = s^2/2 - s\,\Phi^{-1}(\Delta).$$ Put deltas convert as call-equivalent \(\Delta = 1 + \delta_{put}\).

Usage

ec_delta_to_k(delta, s)

Arguments

delta

Call-equivalent delta in (0, 1).

s

Total dispersion at the node (annualized volatility times \(\sqrt{\tau}\)).

Value

Log-forward moneyness \(k = \log(K/F)\).

Examples

ec_delta_to_k(c(0.25, 0.5, 0.75), s = 0.3)
#> [1]  0.2473469  0.0450000 -0.1573469