Pricing relevance of event learning: the sufficient statistic

The single number that decides whether learning about an event is first-order for an asset's option prices: the ratio of learning variance to no-learning variance over the tenor, $$\rho = \frac{[\Delta\eta\; q(1-q)]^2\, A}{\sigma^2 (T-t)}.$$

Usage

ec_relevance(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 $\rho \ge 0$.

Details

The other headline objects are monotone transforms of $\rho$: the variance share of learning is $\rho / (1 + \rho)$ (ec_variance_share()) and the rule-of-thumb IV contribution is $\sigma \rho / 2$ (ec_iv_rule()). Use $\rho$ to screen (event, asset) pairs: FX pairs around elections sit at $\rho \approx 0.002$–$0.01$ (irrelevant to two decimals), single names with large exposures can reach first-order magnitudes.

Examples

# US election 2016, 2W tenor: rho of about 1.1% -> variance share 1.1%
ec_relevance(deta = -0.099, q = 0.172, A = 0.046,
             sigma = 0.19326, tenor = 14 / 365)
#> [1] 0.006383027