Local Volatility

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos
// ------------------------------------------------------------------------------------------------
// Original author:  RicardoSantos
// Original title:   Local Volatility
// Licence:          MPL-2.0 (the header above is the original notice, kept verbatim)
// Pine version:     5
// Fetched:          2026-10-12
// Ported to FloScript by FloSignals; modifications under MPL-2.0.
// Converter:        @flosignals/floscript 0.1.0, strict mode, score 100/100
// ------------------------------------------------------------------------------------------------
//@floscript=1
//@version=5

indicator('Local Volatility')
//The traditional calculation of volatility involves computing the standard deviation of returns,
// which is based on the mean return. However, when the asset price exhibits a trending behavior,
// the mean return could be significantly different from zero, and changing the length of the time
// window used for the calculation could result in artificially high volatility values. This is because
// more returns would be further away from the mean, leading to a larger sum of squared deviations.
// To address this issue, our Local Volatility measure computes the standard deviation of the
// differences between consecutive asset prices, rather than their returns. This provides a measure of
// how much the price changes from one tick to the next, irrespective of the overall trend.
// ref: https://arxiv.org/abs/2308.14235

int length_01 = input(10)
int length_02 = input(15)
int length_03 = input(50)
slv(src, t) => math.sqrt(ta.sma(math.pow(src - src[1], 2.0), t))
clv(src) => math.sqrt(ta.cum(math.pow(src - src[1], 2.0) / (bar_index + 1)))

plot(slv(close, length_01), 'short therm', #ff0000)
plot(slv(close, length_02), 'short therm', #ff4800)
plot(slv(close, length_03), 'short therm', #ff9900)
plot(clv(close), 'long therm', #0080ff)

This file is under the Mozilla Public License 2.0; it is a port of the original by RicardoSantos, with the original licence header kept and the changes made for FloScript noted in the file.

• v22026-10-14

  Library refresh 2026-10-14

• v12026-10-12

  Library refresh 2026-10-12