The volatility risk premium by option tenor, each matched to its own realized window

Run it yourself

This is the exact query behind the result above. Change a ticker, a date or a column and run it against the warehouse — no account, no key. The no-signup tier is smaller than the one this page was computed on; a query that reaches past it comes back saying which plan runs it.

WITH
closes AS
(
    SELECT
        date,
        toFloat64(any(close)) AS px
    FROM global_markets.stocks_daily_aggs
    WHERE ticker = 'SPY'
      AND date >= '2021-06-01'
    GROUP BY date
),
daily_returns AS
(
    SELECT
        date,
        pow(log(px / lagInFrame(px) OVER (ORDER BY date ROWS BETWEEN 1 PRECEDING AND CURRENT ROW)), 2) AS r2
    FROM closes
),
forward_rv AS
(
    SELECT
        date,
        100 * sqrt(252 * avg(r2) OVER (ORDER BY date ROWS BETWEEN 1 FOLLOWING AND 7 FOLLOWING))  AS rv_07_pct,
        100 * sqrt(252 * avg(r2) OVER (ORDER BY date ROWS BETWEEN 1 FOLLOWING AND 15 FOLLOWING)) AS rv_15_pct,
        100 * sqrt(252 * avg(r2) OVER (ORDER BY date ROWS BETWEEN 1 FOLLOWING AND 31 FOLLOWING)) AS rv_31_pct,
        100 * sqrt(252 * avg(r2) OVER (ORDER BY date ROWS BETWEEN 1 FOLLOWING AND 62 FOLLOWING)) AS rv_62_pct,
        count(r2) OVER (ORDER BY date ROWS BETWEEN 1 FOLLOWING AND 62 FOLLOWING)                 AS sessions_ahead
    FROM daily_returns
    WHERE isFinite(r2)
),
by_day AS
(
    SELECT
        g.date AS date,
        multiIf(g.days_to_expiry <= 14, '07-14 days',
                g.days_to_expiry <= 30, '15-30 days',
                g.days_to_expiry <= 60, '31-60 days',
                                        '61-120 days') AS tenor,
        avg(100 * toFloat64(g.implied_volatility))      AS iv_pct,
        any(multiIf(g.days_to_expiry <= 14, f.rv_07_pct,
                    g.days_to_expiry <= 30, f.rv_15_pct,
                    g.days_to_expiry <= 60, f.rv_31_pct,
                                            f.rv_62_pct)) AS rv_pct
    FROM global_markets.options_greeks AS g
    INNER JOIN forward_rv AS f ON f.date = g.date
    WHERE g.underlying_symbol = 'SPY'
      AND g.iv_converged = 1
      AND g.volume > 0
      AND g.days_to_expiry BETWEEN 7 AND 120
      AND abs(toFloat64(g.strike_price) / toFloat64(g.underlying_close) - 1) < 0.05
      AND g.date >= '2021-08-01'
      AND f.sessions_ahead = 62
    GROUP BY date, tenor
    HAVING count() >= 5
)
SELECT
    tenor,
    round(avg(iv_pct), 2)                              AS implied_vol_pct,
    round(avg(rv_pct), 2)                              AS realized_vol_pct,
    round(avg(iv_pct - rv_pct), 2)                     AS premium_pct,
    round(100 * countIf(iv_pct > rv_pct) / count(), 1) AS positive_share_pct
FROM by_day
GROUP BY tenor
ORDER BY tenor