Generalized Black-Scholes-Merton w/ Analytical Greeks [Loxx]Generalized Black-Scholes-Merton w/ Analytical Greeks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The options sensitivities (Greeks) are the partial derivatives of the Black-Scholes-Merton (BSM) formula. Analytical Greeks for our purposes here are broken down into various categories:
Delta Greeks: Delta, DDeltaDvol, Elasticity
Gamma Greeks: Gamma, GammaP, DGammaDSpot/speed, DGammaDvol/Zomma
Vega Greeks: Vega, DVegaDvol/Vomma, VegaP
Theta Greeks: Theta
Rate/Carry Greeks: Rho, Rho futures option, Carry Rho, Phi/Rho2
Probability Greeks: StrikeDelta, Risk Neutral Density
(See the code for more details)
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm , float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm ) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility ( vega ) when searching for the implied volatility . For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility , al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm , lies between CL and cH . The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility . Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv (i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility , E is the desired degree of accuracy, c(m) is the market price of the option, and dc/ dv (i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility ).
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
In den Scripts nach "1995年+黄金价格+历史数据" suchen
Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]Generalized Black-Scholes-Merton Option Pricing Formula is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks aka "Option Sensitivities" and implied volatility calculations. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas".
Black-Scholes-Merton Option Pricing
The BSM formula and its binomial counterpart may easily be the most used "probability model/tool" in everyday use — even if we con- sider all other scientific disciplines. Literally tens of thousands of people, including traders, market makers, and salespeople, use option formulas several times a day. Hardly any other area has seen such dramatic growth as the options and derivatives businesses. In this chapter we look at the various versions of the basic option formula. In 1997 Myron Scholes and Robert Merton were awarded the Nobel Prize (The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel). Unfortunately, Fischer Black died of cancer in 1995 before he also would have received the prize.
It is worth mentioning that it was not the option formula itself that Myron Scholes and Robert Merton were awarded the Nobel Prize for, the formula was actually already invented, but rather for the way they derived it — the replicating portfolio argument, continuous- time dynamic delta hedging, as well as making the formula consistent with the capital asset pricing model (CAPM). The continuous dynamic replication argument is unfortunately far from robust. The popularity among traders for using option formulas heavily relies on hedging options with options and on the top of this dynamic delta hedging, see Higgins (1902), Nelson (1904), Mello and Neuhaus (1998), Derman and Taleb (2005), as well as Haug (2006) for more details on this topic. In any case, this book is about option formulas and not so much about how to derive them.
Provided here are the various versions of the Black-Scholes-Merton formula presented in the literature. All formulas in this section are originally derived based on the underlying asset S follows a geometric Brownian motion
dS = mu * S * dt + v * S * dz
where t is the expected instantaneous rate of return on the underlying asset, a is the instantaneous volatility of the rate of return, and dz is a Wiener process.
The formula derived by Black and Scholes (1973) can be used to value a European option on a stock that does not pay dividends before the option's expiration date. Letting c and p denote the price of European call and put options, respectively, the formula states that
c = S * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(d2) - S * N(d1)
where
d1 = (log(S / X) + (r + v^2 / 2) * T) / (v * T^0.5)
d2 = (log(S / X) + (r - v^2 / 2) * T) / (v * T^0.5) = d1 - v * T^0.5
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
b = Cost of carry
v = Volatility of the underlying asset price
cnd (x) = The cumulative normal distribution function
nd(x) = The standard normal density function
convertingToCCRate(r, cmp ) = Rate compounder
gImpliedVolatilityNR(string CallPutFlag, float S, float x, float T, float r, float b, float cm, float epsilon) = Implied volatility via Newton Raphson
gBlackScholesImpVolBisection(string CallPutFlag, float S, float x, float T, float r, float b, float cm) = implied volatility via bisection
Implied Volatility: The Bisection Method
The Newton-Raphson method requires knowledge of the partial derivative of the option pricing formula with respect to volatility (vega) when searching for the implied volatility. For some options (exotic and American options in particular), vega is not known analytically. The bisection method is an even simpler method to estimate implied volatility when vega is unknown. The bisection method requires two initial volatility estimates (seed values):
1. A "low" estimate of the implied volatility, al, corresponding to an option value, CL
2. A "high" volatility estimate, aH, corresponding to an option value, CH
The option market price, Cm, lies between CL and cH. The bisection estimate is given as the linear interpolation between the two estimates:
v(i + 1) = v(L) + (c(m) - c(L)) * (v(H) - v(L)) / (c(H) - c(L))
Replace v(L) with v(i + 1) if c(v(i + 1)) < c(m), or else replace v(H) with v(i + 1) if c(v(i + 1)) > c(m) until |c(m) - c(v(i + 1))| <= E, at which point v(i + 1) is the implied volatility and E is the desired degree of accuracy.
Implied Volatility: Newton-Raphson Method
The Newton-Raphson method is an efficient way to find the implied volatility of an option contract. It is nothing more than a simple iteration technique for solving one-dimensional nonlinear equations (any introductory textbook in calculus will offer an intuitive explanation). The method seldom uses more than two to three iterations before it converges to the implied volatility. Let
v(i + 1) = v(i) + (c(v(i)) - c(m)) / (dc / dv(i))
until |c(m) - c(v(i + 1))| <= E at which point v(i + 1) is the implied volatility, E is the desired degree of accuracy, c(m) is the market price of the option, and dc/dv(i) is the vega of the option evaluaated at v(i) (the sensitivity of the option value for a small change in volatility).
Numerical Greeks or Greeks by Finite Difference
Analytical Greeks are the standard approach to estimating Delta, Gamma etc... That is what we typically use when we can derive from closed form solutions. Normally, these are well-defined and available in text books. Previously, we relied on closed form solutions for the call or put formulae differentiated with respect to the Black Scholes parameters. When Greeks formulae are difficult to develop or tease out, we can alternatively employ numerical Greeks - sometimes referred to finite difference approximations. A key advantage of numerical Greeks relates to their estimation independent of deriving mathematical Greeks. This could be important when we examine American options where there may not technically exist an exact closed form solution that is straightforward to work with. (via VinegarHill FinanceLabs)
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
STD-Filtered, Adaptive Exponential Hull Moving Average [Loxx]STD-Filtered, Adaptive Exponential Hull Moving Average is a Kaufman Efficiency Ratio Adaptive Hull Moving Average that uses EMA instead of WMA for its computation. I've also added standard deviation stepping to further smooth the signal. Using EMA instead of WMA turns the Hull into what's called the AEHMA. You can read more about the EHMA here: eceweb1.rutgers.edu
What is the traditional Hull Moving Average?
The Hull Moving Average (HMA) attempts to minimize the lag of a traditional moving average while retaining the smoothness of the moving average line. Developed by Alan Hull in 2005, this indicator makes use of weighted moving averages to prioritize more recent values and greatly reduce lag. The resulting average is more responsive and well-suited for identifying entry points.
What is Kaufman's Efficiency Ratio?
The Efficiency Ratio (ER) was first presented by Perry Kaufman in his 1995 book ‘Smarter Trading‘. It is calculated by dividing the price change over a period by the absolute sum of the price movements that occurred to achieve that change. The resulting ratio ranges between 0 and 1 with higher values representing a more efficient or trending market.
The value of the ER ranges between 0 and 1. It has the value of 1 when prices move in the same direction for the full time over which the indicator is calculated, e.g. n bars period. It has a value of 0 when prices are unchanged over the n periods. When prices move in wide swings within the interval, the sum of the denominator becomes very large compared to the numerator and ER approaches zero.
Some uses for ER:
A qualifier for a trend following trade; a trend is considered “persistent” only when RE is above a certain value, e.g. 0.3 or 0.4 .
A filter to screen out choppy stocks/markets, where breakouts are frequently “fakeouts”.
In an adaptive trading system, helping to determine whether to apply a trend following algorithm or a mean reversion algorithm.
It is used in the calculation of Kaufman’s Adaptive Moving Average (KAMA).
How to calculate the Hull Adaptive Moving Average (HAMA)
Find Signal to Noise ratio (SNR)
Normalize SNR from 0 to 1
Calculate adaptive alphas
Apply EMAs
Included
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
TheATR: Aroon Oscillator.Aroon Oscillator (AO).
The Aroon Oscillator, was developed by Tushar Chande, in 1995, to highlight the start of a new trend and to measure trend strength.
I re-branded a bit the whole thing, If you are familiar with how this Oscillator usually is, you are going to notice the differences.
Aroon Oscillator Components.
1 - Aroon Up -> Bullish Directional Component, highlighted in blue.
2 - Aroon Down -> Bearish Directional Component, highlighted in purple.
We also have the Oscillators static thresholds, which are:
- 0 Line.
- 100 Line.
- Exit Signal Line Level.
How to read the Aroon Oscillator.
The AO main goal, is to identify the trend from its first stages, to then come up with how strong that trend is.
So, classic interpretation for the AO would be:
-Aroon Up>Aroon Down = Bull Scenario.
-Aroon Up
Genesis Matrix [Loxx]Over a decade ago, the Genesis Matrix system was one of best strategies for new traders looking to learn how to really trade trends. Fast forward to 2022, a new version of Genesis Matrix has emerged using TVI, CCI, HL Channel & T3
What is T3?
The T3 moving average is an indicator of an indicator since it includes several EMAs of another EMA. Unlike any other moving average, it adds the so-called volume factor, a value between 0 and 1. Like the SMA, traders typically use this indicator to spot trends and trend reversals.
What is CCI?
The Commodity Channel Index ( CCI ) measures the current price level relative to an average price level over a given period of time. CCI is relatively high when prices are far above their average. CCI is relatively low when prices are far below their average. Using this method, CCI can be used to identify overbought and oversold levels.
Genesis matrix uses Jurik-Smoothed CCI w/ MA Deviation--a spin on regular CCI .Usually CCI is calculated as using average ( Simple Moving Average ) and mean deviation. In this version, average is replaced with well known JMA (Jurik Moving Average) instead for the smoothing phase and the deviation is replaced with variety moving average deviation. The result in this one is responsive and fast (as expected) and also it is smoother than the original CCI (as expected).
What is SSL?
Known as the SSL, the Semaphore Signal Level channel chart alert is an indicator that combines moving averages to provide you with a clear visual signal of price movement dynamics. In short, it's designed to show you when a price trend is forming. For our purposes here, SSL has been modified to allow for different moving average selection and different closing price look back periods.
What is William Blau Ergodic Tick Volume?
This is one of the techniques described by William Blau in his book "Momentum, Direction and Divergence" (1995). If you like to learn more, we advise you to read this book. His book focuses on three key aspects of trading: momentum, direction and divergence. Blau, who was an electrical engineer before becoming a trader, thoroughly examines the relationship between price and momentum in step-by-step examples. From this grounding, he then looks at the deficiencies in other oscillators and introduces some innovative techniques, including a fresh twist on Stochastics. On directional issues, he analyzes the intricacies of ADX and offers a unique approach to help define trending and non-trending periods.
William Blau's definition of TVI ergodicity is that the indictor is ergodic when periods are set to 32, 5, 1, and the signal is set to 5. Other combinations are not ergodic, according to Blau.
How to use
Long signal: All 4 indicators turn green
Short signal: All 4 indicators turn red
Included
Bar coloring
William Blau Ergodic Tick Volume Indicator (TVI) [Loxx]William Blau Ergodic Tick Volume Indicator (TVI) is a volume/volatility indicator that is used for finding reversals in price movement
What is William Blau Ergodic Tick Volume?
This is one of the techniques described by William Blau in his book "Momentum, Direction and Divergence" (1995). If you like to learn more, we advise you to read this book. His book focuses on three key aspects of trading: momentum, direction and divergence. Blau, who was an electrical engineer before becoming a trader, thoroughly examines the relationship between price and momentum in step-by-step examples. From this grounding, he then looks at the deficiencies in other oscillators and introduces some innovative techniques, including a fresh twist on Stochastics. On directional issues, he analyzes the intricacies of ADX and offers a unique approach to help define trending and non-trending periods.
William Blau's definition of TVI ergodicity is that the indictor is ergodic when periods are set to 32, 5, 1, and the signal is set to 5. Other combinations are not ergodic, according to Blau.
How to use TVI
TVI bar color change is a signal to enter the market. When the TVI changes from yellow to red, it is a signal to buy and if the TVI bar changes from blue to green, it is a signal to sell.
Just like the MACD and TRIX, the zero line on the indicator determines market sentiment and trend. If the TVI bars are above the zero line it's bullish and if the TVI bars are below the zero line the trend is bearish. Zero line crosses can be used to determine continuation and trend entries as well.
Included
Bar coloring
35+ moving averages for both TVI and the signal
Aroon Oscillator of Adaptive RSI [Loxx]Aroon Oscillator of Adaptive RSI uses RSI to calculate AROON in attempt to capture more trend and momentum quicker than Aroon or RSI alone. Aroon Oscillator of Adaptive RSI has three different types of RSI calculations and the choice of either fixed, VHF Adaptive, or Band-pass Adaptive cycle measures to calculate RSI.
Arron Oscillator:
The Aroon Oscillator was developed by Tushar Chande in 1995 as part of the Aroon Indicator system. Chande’s intention for the system was to highlight short-term trend changes. The name Aroon is derived from the Sanskrit language and roughly translates to “dawn’s early light.”
The Aroon Oscillator is a trend-following indicator that uses aspects of the Aroon Indicator (Aroon Up and Aroon Down) to gauge the strength of a current trend and the likelihood that it will continue.
Aroon oscillator readings above zero indicate that an uptrend is present, while readings below zero indicate that a downtrend is present. Traders watch for zero line crossovers to signal potential trend changes. They also watch for big moves, above 50 or below -50 to signal strong price moves.
Wilders' RSI:
The Relative Strength Index (RSI) is a well versed momentum based oscillator which is used to measure the speed (velocity) as well as the change (magnitude) of directional price movements. Essentially RSI, when graphed, provides a visual mean to monitor both the current, as well as historical, strength and weakness of a particular market. The strength or weakness is based on closing prices over the duration of a specified trading period creating a reliable metric of price and momentum changes. Given the popularity of cash settled instruments (stock indexes) and leveraged financial products (the entire field of derivatives); RSI has proven to be a viable indicator of price movements.
RSX RSI:
RSI is a very popular technical indicator, because it takes into consideration market speed, direction and trend uniformity. However, the its widely criticized drawback is its noisy (jittery) appearance. The Jurk RSX retains all the useful features of RSI, but with one important exception: the noise is gone with no added lag.
Rapid RSI:
Rapid RSI Indicator, from Ian Copsey's article in the October 2006 issue of Stocks & Commodities magazine.
RapidRSI resembles Wilder's RSI, but uses a SMA instead of a WilderMA for internal smoothing of price change accumulators.
VHF Adaptive Cycle:
Vertical Horizontal Filter (VHF) was created by Adam White to identify trending and ranging markets. VHF measures the level of trend activity, similar to ADX DI. Vertical Horizontal Filter does not, itself, generate trading signals, but determines whether signals are taken from trend or momentum indicators. Using this trend information, one is then able to derive an average cycle length.
Band-pass Adaptive Cycle
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal ; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth.
Included:
-Toggle on/off bar coloring
-Customize RSI signal using fixed, VHF Adaptive, and Band-pass Adaptive calculations
-Choose from three different RSI types
Happy trading!
NormalizedOscillatorsLibrary "NormalizedOscillators"
Collection of some common Oscillators. All are zero-mean and normalized to fit in the -1..1 range. Some are modified, so that the internal smoothing function could be configurable (for example, to enable Hann Windowing, that John F. Ehlers uses frequently). Some are modified for other reasons (see comments in the code), but never without a reason. This collection is neither encyclopaedic, nor reference, however I try to find the most correct implementation. Suggestions are welcome.
rsi2(upper, lower) RSI - second step
Parameters:
upper : Upwards momentum
lower : Downwards momentum
Returns: Oscillator value
Modified by Ehlers from Wilder's implementation to have a zero mean (oscillator from -1 to +1)
Originally: 100.0 - (100.0 / (1.0 + upper / lower))
Ignoring the 100 scale factor, we get: upper / (upper + lower)
Multiplying by two and subtracting 1, we get: (2 * upper) / (upper + lower) - 1 = (upper - lower) / (upper + lower)
rms(src, len) Root mean square (RMS)
Parameters:
src : Source series
len : Lookback period
Based on by John F. Ehlers implementation
ift(src) Inverse Fisher Transform
Parameters:
src : Source series
Returns: Normalized series
Based on by John F. Ehlers implementation
The input values have been multiplied by 2 (was "2*src", now "4*src") to force expansion - not compression
The inputs may be further modified, if needed
stoch(src, len) Stochastic
Parameters:
src : Source series
len : Lookback period
Returns: Oscillator series
ssstoch(src, len) Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
Parameters:
src : Source series
len : Lookback period
Returns: Oscillator series
Introduced in the January 2014 issue of Stocks and Commodities
This is not an implementation of MESA Stochastic, as it is based on Highpass filter not present in the function (but you can construct it)
This implementation is scaled by 0.95, so that Super Smoother does not exceed 1/-1
I do not know, if this the right way to fix this issue, but it works for now
netKendall(src, len) Noise Elimination Technology by John F. Ehlers
Parameters:
src : Source series
len : Lookback period
Returns: Oscillator series
Introduced in the December 2020 issue of Stocks and Commodities
Uses simplified Kendall correlation algorithm
Implementation by @QuantTherapy:
rsi(src, len, smooth) RSI
Parameters:
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
vrsi(src, len, smooth) Volume-scaled RSI
Parameters:
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
This is my own version of RSI. It scales price movements by the proportion of RMS of volume
mrsi(src, len, smooth) Momentum RSI
Parameters:
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
rrsi(src, len, smooth) Rocket RSI
Parameters:
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
Inspired by RocketRSI by John F. Ehlers (Stocks and Commodities, May 2018)
Does not include Fisher Transform of the original implementation, as the output must be normalized
Does not include momentum smoothing length configuration, so always assumes half the lookback length
mfi(src, len, smooth) Money Flow Index
Parameters:
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
lrsi(src, in_gamma, len) Laguerre RSI by John F. Ehlers
Parameters:
src : Source series
in_gamma : Damping factor (default is -1 to generate from len)
len : Lookback period (alternatively, if gamma is not set)
Returns: Oscillator series
The original implementation is with gamma. As it is impossible to collect gamma in my system, where the only user input is length,
an alternative calculation is included, where gamma is set by dividing len by 30. Maybe different calculation would be better?
fe(len) Choppiness Index or Fractal Energy
Parameters:
len : Lookback period
Returns: Oscillator series
The Choppiness Index (CHOP) was created by E. W. Dreiss
This indicator is sometimes called Fractal Energy
er(src, len) Efficiency ratio
Parameters:
src : Source series
len : Lookback period
Returns: Oscillator series
Based on Kaufman Adaptive Moving Average calculation
This is the correct Efficiency ratio calculation, and most other implementations are wrong:
the number of bar differences is 1 less than the length, otherwise we are adding the change outside of the measured range!
For reference, see Stocks and Commodities June 1995
dmi(len, smooth) Directional Movement Index
Parameters:
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
Based on the original Tradingview algorithm
Modified with inspiration from John F. Ehlers DMH (but not implementing the DMH algorithm!)
Only ADX is returned
Rescaled to fit -1 to +1
Unlike most oscillators, there is no src parameter as DMI works directly with high and low values
fdmi(len, smooth) Fast Directional Movement Index
Parameters:
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
Same as DMI, but without secondary smoothing. Can be smoothed later. Instead, +DM and -DM smoothing can be configured
doOsc(type, src, len, smooth) Execute a particular Oscillator from the list
Parameters:
type : Oscillator type to use
src : Source series
len : Lookback period
smooth : Internal smoothing algorithm
Returns: Oscillator series
Chande Momentum Oscillator (CMO) is RSI without smoothing. No idea, why some authors use different calculations
LRSI with Fractal Energy is a combo oscillator that uses Fractal Energy to tune LRSI gamma, as seen here: www.prorealcode.com
doPostfilter(type, src, len) Execute a particular Oscillator Postfilter from the list
Parameters:
type : Oscillator type to use
src : Source series
len : Lookback period
Returns: Oscillator series
Projection Oscillator [CC]The Projection Oscillator was created by Mel Widner (Stocks and Commodities Jul 1995) and this is another hidden gem that is of course a great complementary indicator to my previous Projection Bands . I would recommend to use both on the same chart so you get the full array of information. This indicator tells you where the current price falls between the bands and the higher the oscillator is, the closer the price is to the upper band and vice versa. Now since the price never falls outside of the bands, the indicator is limited from 0 to 100. You will notice that with this indicator it gives even earlier signals than the Projection Bands so a very useful indicator indeed. I have included strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color. Buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators or scripts you would like to see me publish!
Projection Bandwidth [CC]The Projection Bandwidth was created by Mel Widner (Stocks and Commodities Jul 1995) and this is another of my series of indicators that I consider undiscovered gems. For those of you who are unaware, the Bandwidth indicator measures the distance between the high and low bands and if you remember from my Projection Bands script, the Projection Bands give pretty accurate early signals of trend reversals and followed fairly closely by a large bulge in the bands. The large bulges in the bands essentially act as the confirmation that the trend reversal is happening and so that brings me to this indicator. This indicator gives signals based on if it has reached a peak or a valley. Both extremes mean that the current trend is ending and I have color coded it based on the buy and sell signals from my Projection Bands indicator. I have included strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color. Buy when the line turns green and sell when it turns red.
Let me know if there are any other scripts or indicators you would like to see me publish!
Projection Bands [CC]The Projection Bands were created by Mel Widner (Stocks and Commodities Jul 1995) and this indicator and the other two that rely on this one (I will publish them later) are very underappreciated in my humble opinion. The biggest strength of this indicator is the fact that it is a leading indicator for dramatic price movements. As you can see in my example chart it consistently gives great exit points before a downturn. I have included strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color. Buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators or scripts you would like to see me publish!
Combo Backtest 123 Reversal & Ergodic TSI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
r - Length of first EMA smoothing of 1 day momentum 4
s - Length of second EMA smoothing of 1 day smoothing 8
u- Length of third EMA smoothing of 1 day momentum 6
Length of EMA signal line 3
Source of Ergotic TSI Close
This is one of the techniques described by William Blau in his book "Momentum,
Direction and Divergence" (1995). If you like to learn more, we advise you to
read this book. His book focuses on three key aspects of trading: momentum,
direction and divergence. Blau, who was an electrical engineer before becoming
a trader, thoroughly examines the relationship between price and momentum in
step-by-step examples. From this grounding, he then looks at the deficiencies
in other oscillators and introduces some innovative techniques, including a
fresh twist on Stochastics. On directional issues, he analyzes the intricacies
of ADX and offers a unique approach to help define trending and non-trending periods.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Ergodic TSI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
r - Length of first EMA smoothing of 1 day momentum 4
s - Length of second EMA smoothing of 1 day smoothing 8
u- Length of third EMA smoothing of 1 day momentum 6
Length of EMA signal line 3
Source of Ergotic TSI Close
This is one of the techniques described by William Blau in his book "Momentum,
Direction and Divergence" (1995). If you like to learn more, we advise you to
read this book. His book focuses on three key aspects of trading: momentum,
direction and divergence. Blau, who was an electrical engineer before becoming
a trader, thoroughly examines the relationship between price and momentum in
step-by-step examples. From this grounding, he then looks at the deficiencies
in other oscillators and introduces some innovative techniques, including a
fresh twist on Stochastics. On directional issues, he analyzes the intricacies
of ADX and offers a unique approach to help define trending and non-trending periods.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Backtest 123 Reversal & Ergodic MDI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book "Momentum,
Direction and Divergence" (1995). If you like to learn more, we advise you to
read this book. His book focuses on three key aspects of trading: momentum,
direction and divergence. Blau, who was an electrical engineer before becoming
a trader, thoroughly examines the relationship between price and momentum in
step-by-step examples. From this grounding, he then looks at the deficiencies
in other oscillators and introduces some innovative techniques, including a
fresh twist on Stochastics. On directional issues, he analyzes the intricacies
of ADX and offers a unique approach to help define trending and non-trending periods.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Ergodic MDI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book "Momentum,
Direction and Divergence" (1995). If you like to learn more, we advise you to
read this book. His book focuses on three key aspects of trading: momentum,
direction and divergence. Blau, who was an electrical engineer before becoming
a trader, thoroughly examines the relationship between price and momentum in
step-by-step examples. From this grounding, he then looks at the deficiencies
in other oscillators and introduces some innovative techniques, including a
fresh twist on Stochastics. On directional issues, he analyzes the intricacies
of ADX and offers a unique approach to help define trending and non-trending periods.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Backtest 123 Reversal & Ergodic MACD This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book
"Momentum, Direction and Divergence" (1995). If you like to learn more,
we advise you to read this book. His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship
between price and momentum in step-by-step examples. From this grounding,
he then looks at the deficiencies in other oscillators and introduces some
innovative techniques, including a fresh twist on Stochastics. On directional
issues, he analyzes the intricacies of ADX and offers a unique approach to help
define trending and non-trending periods.
Blau`s indicator is like usual MACD, but it plots opposite of meaningof
stndard MACD indicator.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Ergodic MACD This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book
"Momentum, Direction and Divergence" (1995). If you like to learn more,
we advise you to read this book. His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship
between price and momentum in step-by-step examples. From this grounding,
he then looks at the deficiencies in other oscillators and introduces some
innovative techniques, including a fresh twist on Stochastics. On directional
issues, he analyzes the intricacies of ADX and offers a unique approach to help
define trending and non-trending periods.
Blau`s indicator is like usual MACD, but it plots opposite of meaningof
stndard MACD indicator.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Backtest 123 Reversal & Ergodic CSI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book
"Momentum, Direction and Divergence" (1995). If you like to learn more,
we advise you to read this book. His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship between
price and momentum in step-by-step examples. From this grounding, he then looks
at the deficiencies in other oscillators and introduces some innovative techniques,
including a fresh twist on Stochastics. On directional issues, he analyzes the
intricacies of ADX and offers a unique approach to help define trending and
non-trending periods.
This indicator plots Ergotic CSI and smoothed Ergotic CSI to filter out noise.
WARNING:
- For purpose educate only
- This script to change bars colors.
Variable Index Dynamic Average VIDYAChande's Variable Index Dynamic Average (VIDYA) is similar to the Exponential Moving Average (EMA), but automatically adjusts the smoothing weight based on price volatility.
VIDYA was developed by Tushar Chande and presented in Technical Analysis of Stocks & Commodities magazine in March 1992.
In the first version, a standard deviation was used as the Volatility Index
Chande modified VIDYA in October 1995 to use a new Chande Momentum Oscillator (CMO) as the Volatility Index.
So I decided to add an option for the users to change the calculation method.
Default calculation is by using Chande's Momentum Oscillator
Users can change the calculation method to Standart Deviation by unchecking the box on the settings menu.
Another option is to fix the CMO length parameter to 9 to make VIDYA more sensitive to price movements.
CMO parameter is defaultly fixed to 9 but users can change the length of the parameter to the VIDYA length by unchecking the relevant box.
As a moving average, VIDYA smooths the market noises and shows the market trends more clearly.
To achieve the goals, the indicator filters out the market fluctuations (noises) by averaging the price values of the periods, over which it is calculated. In the process, some extra value (weight) is added to the average prices, as it is done during calculations of all weighted indicators, such as EMA, LWMA, and SMMA. But during the VIDIYA indicator's calculation, every period's price receives a weight increment adapted to the current market's volatility.
Note that the value of the smoothing factor (k) is calculated with the help of the period's EMA, and increasing or decreasing of the value is achieved by using CMO Chande Momentum Oscillator as a measure of the market's volatility. As a result, the indicator slows down and does not react to the market's volatility when it increases and, on the contrary, speeds up when a strong steady trend takes place.
Note:
Alarm added for color changes.
Hope you use this one at profitable trades.
Combo Strategy 123 Reversal & Ergodic CSI This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This is one of the techniques described by William Blau in his book
"Momentum, Direction and Divergence" (1995). If you like to learn more,
we advise you to read this book. His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship between
price and momentum in step-by-step examples. From this grounding, he then looks
at the deficiencies in other oscillators and introduces some innovative techniques,
including a fresh twist on Stochastics. On directional issues, he analyzes the
intricacies of ADX and offers a unique approach to help define trending and
non-trending periods.
This indicator plots Ergotic CSI and smoothed Ergotic CSI to filter out noise.
WARNING:
- For purpose educate only
- This script to change bars colors.
Moving Average Adaptive QThe Moving Average Adaptive Q (MAAQ) was authored by Perry Kaufman in the Stocks and Commodities Magazine 06/1995
This is similar to his Kaufman Adaptive Moving Average with a few changes. This is a pretty close moving average which I like quite a bit. Try it and let me know what you think.
Send me a message and let me know what other indicators you would like to see!
Combo Backtest 123 Reversal & Directional Trend Index (DTI) This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This technique was described by William Blau in his book "Momentum,
Direction and Divergence" (1995). His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship between
price and momentum in step-by-step examples. From this grounding, he then looks
at the deficiencies in other oscillators and introduces some innovative techniques,
including a fresh twist on Stochastics. On directional issues, he analyzes the
intricacies of ADX and offers a unique approach to help define trending and
non-trending periods.
Directional Trend Index is an indicator similar to DM+ developed by Welles Wilder.
The DM+ (a part of Directional Movement System which includes both DM+ and
DM- indicators) indicator helps determine if a security is "trending." William
Blau added to it a zeroline, relative to which the indicator is deemed positive or
negative. A stable uptrend is a period when the DTI value is positive and rising, a
downtrend when it is negative and falling.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Directional Trend Index (DTI) This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
This technique was described by William Blau in his book "Momentum,
Direction and Divergence" (1995). His book focuses on three key aspects
of trading: momentum, direction and divergence. Blau, who was an electrical
engineer before becoming a trader, thoroughly examines the relationship between
price and momentum in step-by-step examples. From this grounding, he then looks
at the deficiencies in other oscillators and introduces some innovative techniques,
including a fresh twist on Stochastics. On directional issues, he analyzes the
intricacies of ADX and offers a unique approach to help define trending and
non-trending periods.
Directional Trend Index is an indicator similar to DM+ developed by Welles Wilder.
The DM+ (a part of Directional Movement System which includes both DM+ and
DM- indicators) indicator helps determine if a security is "trending." William
Blau added to it a zeroline, relative to which the indicator is deemed positive or
negative. A stable uptrend is a period when the DTI value is positive and rising, a
downtrend when it is negative and falling.
WARNING:
- For purpose educate only
- This script to change bars colors.
