Relative Volatility Index: formula and Pine Script

Formula, smoothing, and boundary conditions

The EMA is a decaying accumulation of directional inputs, not a fixed rolling sum. The code seeds U and D with their first valid inputs, including zero. Both stay uninitialized until σ and the previous close are available. Invalid current inputs leave the stored EMA state unchanged and produce no RVI point.

When U + D is zero, the ratio is undefined. The script plots a gap instead of inventing a neutral 50. A constant series from the start stays undefined; one flat bar after changing prices may have positive σ and therefore still affect the lower branch. Returning 50 or sending flat bars to neither branch would be different, legitimate conventions that must be documented.

For nonnegative U and D with a positive total, RVI is bounded by 0 and 100. At 50 the components are equal. At 80, U = 4D. These are algebraic statements about the formula, not probabilities or estimates of future returns.

Copyable Pine Script with confirmed crossings

//@version=6
indicator("Relative Volatility Index: close / EMA example", overlay = false)

stdLength = input.int(10, "Close standard deviation length", minval = 2)
emaLength = input.int(14, "Directional EMA length", minval = 1)

sigma = ta.stdev(close, stdLength, true)
delta = ta.change(close)
ready = not na(sigma) and not na(delta)
// This variant assigns unchanged closes to the lower branch.
upInput = ready ? (delta > 0 ? sigma : 0.0) : na
downInput = ready ? (delta > 0 ? 0.0 : sigma) : na

// Explicit EMA seed: first valid directional input, including zero.
alpha = 2.0 / (emaLength + 1.0)
var float upper = na
var float lower = na
if ready
    upper := na(upper) ? upInput : alpha * upInput + (1.0 - alpha) * upper
    lower := na(lower) ? downInput : alpha * downInput + (1.0 - alpha) * lower

total = upper + lower
rvi = ready and not na(total) and total > 0 ? 100.0 * upper / total : na
plot(rvi, "RVI", color = color.purple, linewidth = 2, style = plot.style_linebr)
plot(upper, "Upper EMA", display = display.data_window)
plot(lower, "Lower EMA", display = display.data_window)
hline(80, "80 reference", color = color.gray)
hline(50, "Equal components", color = color.gray)
hline(20, "20 reference", color = color.gray)

crossUp = ta.crossover(rvi, 50)
crossDown = ta.crossunder(rvi, 50)
confirmedUp = crossUp and barstate.isconfirmed
confirmedDown = crossDown and barstate.isconfirmed
plotshape(confirmedUp, "Confirmed above 50", shape.triangleup, location.bottom, color.blue, size = size.tiny)
plotshape(confirmedDown, "Confirmed below 50", shape.triangledown, location.top, color.orange, size = size.tiny)
alertcondition(confirmedUp, "RVI above 50", "Relative Volatility Index crossed above 50 on a closed bar.")
alertcondition(confirmedDown, "RVI below 50", "Relative Volatility Index crossed below 50 on a closed bar.")

The purple line can move on an open bar. Blue and orange markers require a completed cross above or below 50 and bar confirmation. Create an alert from the corresponding condition after adding the script to your chart. This script makes no higher-timeframe requests.

Read the ratio without confusing it with trade performance

Above 50 means the upper EMA exceeds the lower EMA. It does not prove that absolute volatility is rising: multiplying both components by the same positive factor leaves RVI unchanged. ATR or the unnormalized standard deviation answers a different question about scale.

A crossing can be a condition to test, but it leaves position size, execution timing, costs, and exits unspecified. For a research specification, one possible rule is to evaluate an upward 50 cross only on a closed bar with close above its 200-bar EMA, then define the next-bar entry, a price-based stop, and a downward-cross exit separately. Those are proposed rules, not results from this example.

Repeated crossings around 50 can create frequent trades in a range. Divergence is also insufficient by itself: the oscillator can weaken while price continues rising. A high RVI does not set a stop distance, and 80 does not mean an 80% chance of a profitable trade. Educational calculation only, not investment advice.

Turn a defined RVI variant into a script with Pineify

Give the Pineify Pine Script AI Coding Agent the calculation contract before asking for alerts or strategy rules. A concrete prompt is: "Use close-price population standard deviation over 10 bars, smooth directional inputs with a 14-period EMA seeded at the first valid input, assign flat closes to the lower branch, return na on a zero total, and confirm 50-level alerts at bar close."

Review the generated source and compare intermediate values bar by bar. If you request a strategy next, specify exits, sizing, fees, and slippage independently. A successful syntax check establishes that the code compiles; it does not establish useful trading performance.

Sources and related indicators

Sources checked October 17, 2026. The formula contract and synthetic table describe the code on this page; the sources provide indicator definitions and Pine bar-confirmation behavior.

• TradingView: Relative Volatility Index
• TradingView: Relative Vigor Index
• TradingView: Average True Range
• TradingView Pine Script: bar states