9A.10 Extracting an event's implied move

Motivation

RBI policy decisions, the Union Budget, election results, quarterly results for a stock, and US data releases (CPI, FOMC) are scheduled. If the market expects a large move on the day, the options that include that day are priced with extra variance. Separating that extra variance from ordinary daily variance is how a desk reads "what the market expects from the event".

Model Ordinary variance accrues at rate $\sigma_d^2$ per year. The event adds a single variance $e$ (in log-return units) on its day. An expiry that includes the event has total variance $w=\sigma_d^2\tau+e$ ; one that does not has $w=\sigma_d^2\tau$ . Dubinsky, Johannes, Kaeck and Seeger (2019) develop estimators of this kind for earnings announcements and find the anticipated announcement uncertainty large, time-varying and informative about future volatility.

9A.10.1Two expiries after the event#

Proposition 9A.9two expiries after the event

If both expiries $\tau_1<\tau_2$ include the event,

e=\frac{\tau_1\tau_2\,(\sigma_1^2-\sigma_2^2)}{\tau_2-\tau_1},\qquad \sigma_d^2=\frac{\sigma_2^2\tau_2-\sigma_1^2\tau_1}{\tau_2-\tau_1}. \tag{9A.13}

The event's standard deviation is $\sqrt e$ and its expected absolute move $\sqrt e\sqrt{2/\pi}$ ; on the event day the total standard deviation is $\sqrt{\sigma_d^2\delta+e}$ with $\delta$ the length of one day.

Proof

Subtract $\sigma_1^2\tau_1=\sigma_d^2\tau_1+e$ from $\sigma_2^2\tau_2=\sigma_d^2\tau_2+e$ : $\sigma_d^2(\tau_2-\tau_1)=\sigma_2^2\tau_2-\sigma_1^2\tau_1$ . Then $e=\sigma_1^2\tau_1-\sigma_d^2\tau_1=\frac{\sigma_1^2\tau_1(\tau_2-\tau_1)-\tau_1(\sigma_2^2\tau_2-\sigma_1^2\tau_1)}{\tau_2-\tau_1}=\frac{\tau_1\tau_2(\sigma_1^2-\sigma_2^2)}{\tau_2-\tau_1}$ . The moments follow from (9A.9) applied to a mean-zero normal event return.∎

So an event shows up as a downward-sloping segment: the near expiry, in which the event is a larger share of total variance, has the higher IV. $e>0$ iff $\sigma_1>\sigma_2$ .

9A.10.2One expiry before, one after#

Proposition 9A.10one expiry before, one after

If $\tau_b$ expires before the event and $\tau_a$ after it, and $\sigma_d$ is the ordinary vol between them,

e=\sigma_a^2\tau_a-\sigma_b^2\tau_b-\sigma_d^2(\tau_a-\tau_b). \tag{9A.14}

Proof

$w_a-w_b$ is the variance accrued between the expiries: $\sigma_d^2(\tau_a-\tau_b)+e$ .∎

This form needs an outside estimate of $\sigma_d$ , the usual choice being the forward vol between two later expiries; with $\sigma_d$ estimated from (9A.12) it reduces to a three-expiry version of (9A.13).

9A.10.3Confounds in the term structure#

What can go wrong The model assumes ordinary variance accrues at a constant rate. Any other source of slope in the term structure is read as an event:

Mean reversion of volatility. After a shock, short-dated IV is above long-dated IV because volatility is expected to decay. (9A.13) reads that slope as an event premium.
Weekends and holidays inside one expiry and not the other (9A.9).
Expiry-day effects in the nearest series.
Skew and the choice of strike. Use ATM-forward strikes for every expiry.
Several events in the window (an RBI decision and a US CPI release in the same week).

Under these confounds the estimate can be negative (no detectable premium) or spuriously positive. Report the inputs, not just $e$ .

9A.10.4The RBI decision of 7 Oct 2026#

Worked example 9A.5RBI MPC decision, 7 Oct 2026

The RBI raised the repo rate by 25 bp to 5.50% on Wednesday 7 Oct 2026 (M11 · 11.7.1). Both the 13 Oct and 27 Oct expiries include that day.

From the 5 Oct chains (13 Oct: 8 days, 14.46%; 27 Oct: 22 days, 14.04%): $e=4.12\times10^{-5}$ , so $\sqrt e=0.64\%$ (145 Nifty points at 22,556) and $\sigma_d=13.79\%$ , a calendar-day standard deviation of 0.72%. Event-day standard deviation $\sqrt{0.72\%^2+0.64\%^2}=0.97\%$ .
From the 6 Oct chains (13 Oct: 7 days, 12.15%; 27 Oct: 21 days, 12.55%): $e=-2.8\times10^{-5}$ . The term structure slopes upward; no event premium is detectable.

The two days give opposite answers, and the 5 Oct curve was inverted from its very front (the 1-day option at 17.2%), which is the mean-reversion confound of item 1 rather than an RBI premium. The honest reading is that the options market did not price the RBI decision as a large distinct event. The realised move fits: the Nifty fell from 22,776.10 to 22,603.05 on 7 Oct, $-0.76\%$ (NSE F&O bhavcopy UndrlygPric), less than one event-day standard deviation even on the 5 Oct estimate. The 13 Oct ATM IV fell from 12.15% to 11.87% on the day, a small post-event decline. The larger move came on 8 Oct ( $-1.64\%$ ), with no scheduled domestic event.

Compare M02 · 2.10.3: before the 4 Jun 2024 election results, India VIX near 24–25 against realised daily volatility of 0.72% implied an event-day standard deviation of about 6.3%, and the realised move was $-6.1\%$ . Some events are priced as jumps; a 25 bp rate decision that was widely expected is not.