Rule of thumb: implied-volatility contribution of event learning

The paper's four-lever rule of thumb for the ATM implied-volatility contribution of learning ahead of a scheduled event: $$\Delta \mathrm{IV} \approx \frac{[\Delta\eta\; q(1-q)]^2\, A}{2\,\sigma\,(T-t)}.$$

Usage

ec_iv_rule(deta, q, A, sigma, tenor)

Arguments

deta: Numeric, the event exposure $\Delta\eta = \eta_1 - \eta_2$.
q: Numeric vector of current event probabilities in $(0,1)$.
A: Numeric vector of event-clock time (non-negative).
sigma: Numeric, annualized no-learning volatility (decimal, e.g. 0.19 for 19%).
tenor: Numeric, option tenor $T - t$ in years.

Value

Numeric vector, the IV contribution in decimal volatility units.

Details

The four levers: the event exposure $\Delta\eta$ (squared), the movability of the probability $q(1-q)$ (squared), the event-clock time $A$, and the dilution by the no-learning volatility and tenor.

Units and the $\sigma$ convention. With sigma as decimal annualized volatility and tenor in years, the result is a decimal volatility increment; multiply by 100 for annualized percentage points. Use the tenor-specific no-learning ATM volatility for sigma; using a different maturity's volatility changes the result mechanically (e.g. the Brexit 2W contribution is 0.007 IV points with the 2W ATM of 10.59% but 0.008 with 9.325%).

Examples

# US election 2016, 2W: about 0.062 annualized IV percentage points
100 * ec_iv_rule(deta = -0.099, q = 0.172, A = 0.046,
                 sigma = 0.19326, tenor = 14 / 365)
#> [1] 0.06167919