Log Contract Ln(S) [Loxx]A log contract, first introduced by Neuberger (1994) and Neuberger (1996), is not strictly an option. It is, however, an important building block in volatility derivatives (see Chapter 6 as well as Demeterfi, Derman, Kamal, and Zou, 1999). The payoff from a log contract at maturity T is simply the natural logarithm of the underlying asset divided by the strike price, ln(S/ X). The payoff is thus nonlinear and has many similarities with options. The value of this contract is (via "The Complete Guide to Option Pricing Formulas")
L = e^(-r * T) * (log(S/X) + (b-v^2/2)*T)
The delta of a log contract is
delta = (e^(-r*T) / S)
and the gamma is
gamma = (e^(-r*T) / S^2)
An even simpler version of the log contract is when the payoff simply is ln(S). The payoff is clearly still nonlinear in the underlying asset. It follows that the value of this contract is:
L = e^(-r * T) * (log(S) + (b-v^2/2)*T)
The theta/time decay of a log contract is
theta = - 1/T * v^2
and its exposure to the stock price, delta, is
delta = - 2/T * 1/S
This basically tells you that you need to be long stocks to be delta- neutral at any time. Moreover, the gamma is
gamma = 2 / (T * S^2)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = volatility of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Komut dosyalarını "Futures" için ara
Powered Option [Loxx]At maturity, a powered call option pays off max(S - X, 0)^i and a put pays off max(X - S, 0)^i . Esser (2003 describes how to value these options (see also Jarrow and Turnbull, 1996, Brockhaus, Ferraris, Gallus, Long, Martin, and Overhaus, 1999). (via "The Complete Guide to Option Pricing Formulas")
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = volatility of the underlying asset price
i = power
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
combin(x) = Combination function, calculates the number of possible combinations for two given numbers
convertingToCCRate(r, cmp ) = Rate compounder
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
Capped Standard Power Option [Loxx]Power options can lead to very high leverage and thus entail potentially very large losses for short positions in these options. It is therefore common to cap the payoff. The maximum payoff is set to some predefined level C. The payoff at maturity for a capped power call is min . Esser (2003) gives the closed-form solution: (via "The Complete Guide to Option Pricing Formulas")
c = S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * (N(e1) - N(e3)) - e^(-r*T) * (X*N(e2) - (C + X) * N(e4))
while the value of a put is
e1 = (log(S/X^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e3 = (log(S/(C + X)^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e4 = e3 - i * v * T^0.5
In the case of a capped power put, we have
p = e^(-r*T) * (X*N(-e2) - (C + X) * N(-e4)) - S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * (N(-e1) - N(-e3))
where e1 and e2 is as before. e3 and e4 has to be changed to
e3 = (log(S/(X - C)^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
e4 = e3 - i * v * T^0.5
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
i = power
c = Capped on pay off
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Standard Power Option [Loxx]Standard power options (aka asymmetric power options) have nonlinear payoff at maturity. For a call, the payoff is max(S^i - X, 0), and for a put, it is max(X - S^i , 0), where i is some power (i > 0). The value of this power call is given by (see Heynen and Kat, 1996c; Zhang, 1998; and Esser, 2003). (via "The Complete Guide to Option Pricing Formulas")
c = S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * N(d1) - X*e^(-r*T) * N(d2)
while the value of a put is
p = X*e^(-r*T) * N(-d2) - S^i * (e^((i - 1) * (r + i*v^2 / 2) - i * (r - b))*T) * N(-d1)
where
d1 = (log(S/X^(1/i)) + (b + (i - 1/2)*v^2)*T) / v*T^0.5
d2 = d1 - i * v * T^0.5
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
pwr = power
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Power Contract [Loxx]There are two main categories of power options. Standard power options' payoff depends on the price of the underlying asset raised to some power. For powered options, the "standard" payoff (stock price in excess of the exercise price) is raised to some power.
A power contract is a simple derivative instrument paying (S/ X)^i at maturity, where i is some fixed power. The value of such a power contract is given by Shaw (1998) as: (via "The Complete Guide to Option Pricing Formulas")
VPower = (S/X)^i * e^((b-v^2)/2)*i - r + i^2 * v^2/2)*T
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
lambda = Jump rate per year
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Moneyness Options [Loxx]A moneyness option is basically a plain vanilla option where the strike is set to a percentage of the future/forward price. For example, a 120% moneyness call would have a strike equal to 120% of the forward price. A 120% moneyness put would have a spot equal to 120% of the strike. The value of this option is given in percent of the forward. The value of a moneyness call or put is thus given by: (via "The Complete Guide to Option Pricing Formulas")
c = p = c^-rT * (N(d1) - LN(d2))
where L = X/F for a call and L = F/X for a put, and
d1 = (-log(L) + v^2*T/2) / (v*T^0.5)
d2 = d1 - (v*T^0.5)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
lambda = Jump rate per year
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Forward Start Options [Loxx]A forward start option with time to maturity T starts at-the-money or proportionally in- or out-of-the-money after a known elapsed time t in the future. The strike is set equal to a positive constant a times the asset price S after the known time t. If a is less than unity, the call (put) will start 1 - a percent in-the-money (out-of-the- money); if a is unity, the option will start at-the-money; and if a is larger than unity, the call (put) will start a - 1 percentage out-of-the- money (in-the-money).A forward start option can be priced using the Rubinstein (1990) formula: (via "The Complete Guide to Option Pricing Formulas")
c = S*e^(b-r)t * (e^(b-r)(T-t) * N(d1)) - alpha * e^-r(T-t) * N(d2))
p = S*e^(b-r)t * (alpha*e^r(T-t) * N(-d2)) - e^-(b-r)(T-t) * N(-d1))
where
d1 = (log(1/alpha) + (b + v^2/2)(T-1))/v*(T-t)^0.5
d2 = d1 - v*(T-t)^0.5
Application
Employee options are often of the forward starting type. Ratchet options (aka cliquet options) consist of a series of forward starting options.
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
a = Alpha
T1 = Time to forward start
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
v = volatility of the underlying asset price
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
Executive Stock Options [Loxx]The Jennergren and Naslund (1993) formula takes into account that an employee or executive often loses her options if she has to leave the company before the option's expiration: (via "The Complete Guide to Option Pricing Formulas")
c = e^(-lambda*T) * (Se^((b-r)T) * N(d1) - Xe^-rT * N(d2))
p = e^(-lambda*T) * (Xe^(-rT) * N(-d2) - Se^(b-r)T * N(-d1))
where
d1 = (log(S/X) + (b + v^2/2)T) / vT^0.5
d2 = d1 - vT^0.5
lambda is the jump rate per year. The value of the executive option equals the ordinary Black-Scholes option price multiplied by the probability e —AT that the executive will stay with the firm until the option expires.
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
lambda = Jump rate per year
cnd1(x) = Cumulative Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Perpetual American Options [Loxx]Perpetual American Options is Perpetual American Options pricing model. This indicator also includes numerical greeks.
American Perpetual Options
While there in general is no closed-form solution for American options (except for non-dividend-paying stock call options) it is possible to find a closed-form solution for options with an infinite time to expiration. The reason is that the time to expiration will always be the same: infinite. The time to maturity, therefore, does not depend on at what point in time we look at the valuation problem, which makes the valuation problem independent of time McKean (1965) and Merton (1973) gives closed-form solutions for American perpetual options. For a call option we have
c = (X / (y1 - 1)) * ((y1 - 1)/y1 * S/X)^y1
where
y1 = 1/2 - b/v^2 + ((b/v^2 - 1/2)^2 + 2*r/v^2)^0.5
If b >= r, then there is never optimal to exercise a call option. In the case of an American perpetual put, we have
p = X/(1-y2) * (((y2 - 1) / y2) * S/X)^y2
where
y2 = 1/2 - b/v^2 - ((b/v^2 - 1/2)^2 + 2*r/v^2)^0.5
In practice, one can naturally discuss if there is such a thing as infinite time to maturity. For instance, credit risk could play an important role: Even when you are buying an option from an AAA bank, there is no guarantee the bank will be around forever.
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
cbnd3(x) = Cumulative Bivariate Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
American Approximation Bjerksund & Stensland 2002 [Loxx]American Approximation Bjerksund & Stensland 2002 is an American Options pricing model. This indicator also includes numerical greeks. You can compare the output of the American Approximation to the Black-Scholes-Merton value on the output of the options panel.
The Bjerksund & Stensland (2002) Approximation
The Bjerksund and Stensland (2002) approximation divides the time to maturity into two parts, each with a separate flat exercise boundary. It is thus a straightforward generalization of the Bjerksund-Stensland 1993 algorithm. The method is fast and efficient and should be more accurate than the Barone-Adesi and Whaley (1987) and the Bjerksund and Stensland (1993b) approximations. The algorithm requires an accurate cumulative bivariate normal approximation. Several approximations that are described in the literature are not sufficiently accurate, but the Genze algorithm works.
C = alpha2*S^B - alpha2*phi(S, t1, B, I2, I2)
+ phi(S, t1, I2, I2) - phi(S, t1, I, I1, I2)
- X*phi(S, t1, 0, I2, I2) + X*phi(S, t1, 0, I1, I2)
+ alpha1*phi(X, t1, B, I1, I2) - alpha1*psi*St, T, B, I1, I2, I1, t1)
+ psi(S, T, 1, I1, I2, I1, t1) - psi(S, T, 1, X, I2, I1, t1)
- X*psi(S, T, 0, I1, I2, I1, t1) + psi(S, T, 0 ,X, I2, I1, t1)
where
alpha1 = (I1 - X)*I1^-B
alpha2 = (I2 - X)*I2^-B
B = (1/2 - b/v^2) + ((b/v^2 - 1/2)^2 + 2*(r/v^2))^0.5
The function psi(S, T, y, H, I) is given by
psi(S, T, gamma, H, I) = e^lambda * S^gamma * (N(-d) - (I/S)^k * N(-d2))
d = (log(S/H) + (b + (gamma - 1/2) * v^2) * T) / (v * T^0.5)
d2 = (log(I^2/(S*H)) + (b + (gamma - 1/2) * v^2) * T) / (v * T^0.5)
lambda = -r + gamma * b + 1/2 * gamma * (gamma - 1) * v^2
k = 2*b/v^2 + (2 * gamma - 1)
and the trigger price I is defined as
I1 = B0 + (B(+infi) - B0) * (1 - e^h1)
I2 = B0 + (B(+infi) - B0) * (1 - e^h2)
h1 = -(b*t1 + 2*v*t1^0.5) * (X^2 / ((B(+infi) - B0))*B0)
h2 = -(b*T + 2*v*T^0.5) * (X^2 / ((B(+infi) - B0))*B0)
t1 = 1/2 * (5^0.5 - 1) * T
B(+infi) = (B / (B - 1)) * X
B0 = max(X, (r / (r - b)) * X)
Moreover, the function psi(S, T, gamma, H, I2, I1, t1) is given by
psi(S, T, gamma, H, I2, I1, t1, r, b, v) = e^(lambda * T) * S^gamma * (M(-e1, -f1, rho) - (I2/S)^k * M(-e2, -f2, rho)
- (I1/S)^k * M(-e3, -f3, -rho) + (I1/I2)^k * M(-e4, -f4, -rho))
where (see screenshot for e and f values)
b=r options on non-dividend paying stock
b=r-q options on stock or index paying a dividend yield of q
b=0 options on futures
b=r-rf currency options (where rf is the rate in the second currency)
Inputs
S = Stock price.
K = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
c = Cost of Carry
V = Variance of the underlying asset price
cnd1(x) = Cumulative Normal Distribution
cbnd3(x) = Cumulative Bivariate Normal Distribution
nd(x) = Standard Normal Density Function
convertingToCCRate(r, cmp ) = Rate compounder
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
Garman and Kohlhagen (1983) for Currency Options [Loxx]Garman and Kohlhagen (1983) for Currency Options 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". This version of BSMOPM is to price Currency Options. 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, Speed
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 for Currency Options
The Garman and Kohlhagen (1983) modified Black-Scholes model can be used to price European currency options; see also Grabbe (1983). The model is mathematically equivalent to the Merton (1973) model presented earlier. The only difference is that the dividend yield is replaced by the risk-free rate of the foreign currency rf:
c = S * e^(-rf * T) * N(d1) - X * e^(-r * T) * N(d2)
p = X * e^(-r * T) * N(-d2) - S * e^(-rf * T) * N(-d1)
where
d1 = (log(S / X) + (r - rf + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - v * T^0.5
For more information on currency options, see DeRosa (2000)
Inputs
S = Stock price.
X = Strike price of option.
T = Time to expiration in years.
r = Risk-free rate
rf = Risk-free rate of the foreign currency
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
Related indicators:
BSM OPM 1973 w/ Continuous Dividend Yield
Black-Scholes 1973 OPM on Non-Dividend Paying Stocks
Generalized Black-Scholes-Merton w/ Analytical Greeks
Generalized Black-Scholes-Merton Option Pricing Formula
Sprenkle 1964 Option Pricing Model w/ Num. Greeks
Modified Bachelier Option Pricing Model w/ Num. Greeks
Bachelier 1900 Option Pricing Model w/ Numerical Greeks
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
Ichimoku Breakout Kumo SWING TRADER (By Insert Cheese)A simple strategy for long spot or long futures (swing traders) based on a basic method of Ichimoku Kinko Hyo strategies.
The strategy is simple:
- Buy when the price breaks the cloud
- Close the trade when the price closes again inside the cloud.
The parameters that work best on this strategy are 10,30,60,30 and 1 for Senkou-Span A
but you can try classic Ichimoku parameters (9,26,52,26,26) or whatever you want like (7,22,44,22,22), (10,30,60,30,30) and others.
-1D chart
I have removed everything from the interface except the cloud to make it visually more aesthetic :D (but if you want to see all the ichimoku indicator you can put in again into the chart)
I have also added several functions for you to do your own backtesting:
- Date range
- TP AND SL method
- Includes long or short trades
The strategy starts with 500 $ and use 100% for trade to make the power of the compounding :P
Remember that this is for only educational porpouse and you must to do your own research and backtested on your usually market..
I hope you like it enjoy and support this indicator :)
Donate (BEP20) 0xC118f1ffB3ac40875C13B3823C182eA2Af344c6d
FrostyBotLibrary "FrostyBot"
JSON Alert Builder for FrostyBot.js Binance Futures and FTX orders
github.com
More Complete Version Soon.
TODO: Comment Functions and annotations from command reference ^^
TODO: Add additional whitelist and symbol mappings.
leverage()
buy()
sell()
cancelall()
closelong()
closeshort()
traillong()
trailshort()
long()
short()
takeprofit()
stoploss()
Volume Weighted Reversal BandsThis is a vwap & vwma hybrid with upper & lower deviation bands that provide excellent price channels and reversal areas. It can be used on lower & higher timeframes, just increase the deviation % for higher timeframes. Try out the 1 minute timeframe with .5% deviation for great scalping levels.
Here is the calculation used for the main line.
(VWMA100 + VWMA500 + VWMA1000 + VWAP) / 4
So it combines 3 VWMAs with the VWAP and divides that number by 4 to give us a moving average. Then we add new levels above and below that moving average to get our channels. The channels are separated by the % deviation you choose in the settings. For tighter bands, lower the percentage deviation and for wider bands, increase the percentage deviation.
The fattest line in the middle is the main moving average and you can expect price to regularly return to this level. The thick lines are the main moving average plus or minus the percentage deviation you have set. There are 10 levels in each direction from the main moving average. The is also a thin short term moving average as well with a custom calculation. It takes 4 different length moving averages that are weighted and 4 more that are volume weighted and divides the total by 8.The lines will be green when price is above the line and red when price is below the line. The thin white line is the VWAP on its own.
These lines will act as dynamic support and resistance so you can scalp them back and forth. These levels work so well because they are volume weighted and the algos hedge their positions back and forth constantly.
For best results, use this indicator on tickers with the highest volume and trading action as the price will stick to these levels better when the big money players are hedging. Some great tickers for this indicator are APPL, SPY, BTC, ETH.
All colors and linewidths can be customized in the settings easily as well as turning off the VWAP or short moving average and adjusting the percentage deviation for the channels.
***MARKETS***
This indicator can be used on all markets, including stocks, crypto, futures and forex.
***TIMEFRAMES***
This indicator can be used on all timeframes.
***TIPS***
Try using numerous indicators of ours on your chart for extra confirmation. Our favorites to pair with these bands are the Scalper Ribbon and Trend Friend Signals. The 3 combined give you a lot of extra confirmation on whether the market is going to reverse at these levels.
MTF TMOTMO - (T)rue (M)omentum (O)scillator) MTF (Higher Aggregation) Version
TMO calculates momentum using the DELTA of price. Giving a much better picture of the trend, reversals & divergences than most momentum oscillators using price. Aside from the regular TMO, this study combines four different TMO aggregations into one indicator for an even better picture of the trend. Once you look deeper into this study you will realize how complex this tool is. This version also produce much more information like crosses, divergences, overbought / oversold signals, higher aggregation fades etc. It is probably not even possible to explain them all, there could easily be an entire e-book about this study.
I have been using this tool for a couple of years now, and this is what i have learned so far:
Favorite Time Frame Variations:
1. 1m / 5m / 30m - Great for intraday futures or options scalps. 30m TMO serves as the overall trend gauge for the day. 5min dictates the longer term intraday moves as well as direction of the 1min. 1min is for the scalps. When the 5min TMO is sloping higher focus should be on 1min buy signals (red to green cross) and vice versa for the 5min agg. sloping down.
2. 5m / 30m / 60m - Also an interesting variation for day trading the 3-5 min charts. Producing more cleaner & beginner-friendly signals that lasts couple of minutes instead of seconds.
3. 120m / Day / 2 Day - For the 30m to 1H or 2H timeframes. Daily & 2 Day dictates the overall trend. 120 min for the signals. Great for a multi-day swings.
4. Day / 2 Day / Week - Good for the daily charts, swing trading analysis as the weekly dictates the overall trend, daily dictates the signals and the 2 day cleans out the daily signals. If the daily & 2 day are not aligned togather, daily signal means nothing. Weekly dictates 2 day - 2 day dictates daily.
5. Week / Month / 3 Month - Same thing as the previous variation but for the weekly charts.
TMO Length:
The default vanilla settings are 14,5,3. Some traders prefer 21,5,3 as the TMO length is litle higher = TMO will potenially last little longer which could teoretically produce less false signals but slower crosses which means signals will lag more behind price. The lower the length, the faster the oscillator oscillates. It is the noice vs. the lag debate. The Length can be changed, but i would not personally touch the other two. Few points up or down on length will not drastically change much. But changes on Calc Length and Smooth Length can produce totally different signals from the original.
Tips & Tricks:
1. Observe
- This is the best tip & trick I can give you. The #1 best way to learn how any study operates is to just observe how it works in certain situations from the past. MTF TMO is not
an exception.
2. The Power of the Higher Aggregation
- The higher aggregation ALWAYS dictates the lower one. Best way to see this? Just 2x the current timeframe aggregation = so on daily chart, plot the daily & two day TMOs and you will notice how the higher agg. smooths out the current agg. The higher the aggregation is, the smoother (but slower) will the TMO turn. The real power kicks in when the 3 or 4 aggregations are aligned togather in one direction.
3. Position of the Higher Aggregation in Relation to the Extremes
- Overbought / oversold signals might not really work on the current aggregation. But pay attention to the higher aggregations in relation to the extremes. Ex: on the daily chart - daily TMO inside the OB / OS extremes might not mean much. But once the higher aggregations such as 3 day or Weekly TMO enters OB/OS zone togather with the daily, this can be a very powerful signal for a TMO reversion to the zeroline.
4. Crosses
- Yes, crosses do work. Personally, I never really focused on them. The thing about the crosses is that it is crucial to pick the right higher aggregation to the combination of the current one that would be reliable but also print enough signals. The closer the cross is to the OB / OS extremes, the more bigger move can occur. Crosses around the zero line can be considered as less quality crosses.
5. Divergences
- TMO can print awesome divergences. The best divergences are on the current aggregation (TMO agg. same as the chart) since the current agg. oscillates fast, it can usually produce lower lows & higher highs faster then any higher aggregations. Easy setup: wait for the higher aggregation to reach the OB / OS extremes and watch the current (chart) aggregation to print a divergence.
6. Three is Enough
- I personally find more than three aggregations messy and hard to read. But there is always the option to turn on the 4th one. Just switch the TMO 4 Main, TMO 4 Signal and TMO 4 Fill in the style settings.
Hope it helps.
FDI-Adaptive Supertrend w/ Floating Levels [Loxx]FDI-Adaptive Supertrend w/ Floating Levels is a Fractal Dimension Index adaptive Supertrend indicator. This allows Supertrend to better adaptive to volatility of the market. This also includes floating levels that act as support and resistance, stop loss or take profit, or indication of market reversal. Additional signal types will be added in the future based on these floating levels.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What is the Supertrend?
Supertrend indicator was created by Olivier Seban to work on different time frames. It works for futures , forex, and equities. It is used in 15 minutes, hourly, weekly, and daily charts . Based on the parameters of multiplier and period, the indicator normally uses 3 for multiplier and 7 for the ATR period as default values. Average True Range is represented by the number of days while the multiplier is the value by which the range is multiplied.
Included:
Bar coloring
Alerts
Signals
Supertrend B&SSuperTrend is one of the most common ATR based trailing stop indicators.
In this version you can change the ATR calculation method from the settings. Default method is RMA, when the alternative method is SMA .
The indicator is easy to use and gives an accurate reading about an ongoing trend. It is constructed with two parameters, namely period and multiplier. The default values used while constructing a superindicator are 10 for average true range or trading period and three for its multiplier.
The average true range (ATR) plays an important role in 'Supertrend' as the indicator uses ATR to calculate its value. The ATR indicator signals the degree of price volatility .
The buy and sell signals are generated when the indicator starts plotting either on top of the closing price or below the closing price. A buy signal is generated when the ‘Supertrend’ closes above the price and a sell signal is generated when it closes below the closing price.
It also suggests that the trend is shifting from descending mode to ascending mode. Contrary to this, when a ‘Supertrend’ closes above the price, it generates a sell signal as the colour of the indicator changes into red.
A ‘Supertrend’ indicator can be used on equities, futures or forex, or even crypto markets and also on daily, weekly and hourly charts as well, but generally, it fails in a sideways-moving market.
SGX Nifty OHLC for Nifty 50 IndexSGX Nifty OHLC for Nifty 50 Index
What is this Indicator?
• This indicator calculates the OHLC levels of SGX Nifty.
How does SGX Nifty impact NIFTY and the Indian Market?
• Helps in predicting NIFTY50 Index behavior.
• The closing price of today's 9.14 am (IST) SGX Nifty will be the Open of today's Nifty50 Open. This helps to determine the opening Gap of Nifty50.
• SGX Nifty OHLC levels can act as support and resistance in Nifty50.
Who to use?
• Beneficial for Day Traders, who trade in NIFTY Index.
What timeframe to use?
• Use 1 minute for better accuracy.
• Other timeframes will also work.
Important Note
• Use 1 min timeframe for accurate OHLC.
• In other timeframes OHLC will have negligible difference, it won't be huge.
• This indicator will appear only on NIFTY Index and Futures chart.
• To hide the warning label go to the indicator Menu.
STD-Filtered, ATR-Adaptive Laguerre Filter [Loxx]STD-Filtered, ATR-Adaptive Laguerre Filter is a standard Laguerre Filter that is first made ATR-adaptive and the passed through a standard deviation filter. This helps reduce noise and refine the output signal. Can apply the standard deviation filter to the price, signal, both or neither.
What is the Laguerre Filter?
The Laguerre RSI indicator created by John F. Ehlers is described in his book "Cybernetic Analysis for Stocks and Futures". The Laguerre Filter is a smoothing filter which is based on Laguerre polynomials. The filter requires the current price, three prior prices, a user defined factor called Alpha to fill its calculation. Adjusting the Alpha coefficient is used to increase or decrease its lag and it's smoothness.
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Ehlers Linear Extrapolation Predictor [Loxx]Ehlers Linear Extrapolation Predictor is a new indicator by John Ehlers. The translation of this indicator into PineScript™ is a collaborative effort between @cheatcountry and I.
The following is an excerpt from "PREDICTION" , by John Ehlers
Niels Bohr said “Prediction is very difficult, especially if it’s about the future.”. Actually, prediction is pretty easy in the context of technical analysis. All you have to do is to assume the market will behave in the immediate future just as it has behaved in the immediate past. In this article we will explore several different techniques that put the philosophy into practice.
LINEAR EXTRAPOLATION
Linear extrapolation takes the philosophical approach quite literally. Linear extrapolation simply takes the difference of the last two bars and adds that difference to the value of the last bar to form the prediction for the next bar. The prediction is extended further into the future by taking the last predicted value as real data and repeating the process of adding the most recent difference to it. The process can be repeated over and over to extend the prediction even further.
Linear extrapolation is an FIR filter, meaning it depends only on the data input rather than on a previously computed value. Since the output of an FIR filter depends only on delayed input data, the resulting lag is somewhat like the delay of water coming out the end of a hose after it supplied at the input. Linear extrapolation has a negative group delay at the longer cycle periods of the spectrum, which means water comes out the end of the hose before it is applied at the input. Of course the analogy breaks down, but it is fun to think of it that way. As shown in Figure 1, the actual group delay varies across the spectrum. For frequency components less than .167 (i.e. a period of 6 bars) the group delay is negative, meaning the filter is predictive. However, the filter has a positive group delay for cycle components whose periods are shorter than 6 bars.
Figure 1
Here’s the practical ramification of the group delay: Suppose we are projecting the prediction 5 bars into the future. This is fine as long as the market is continued to trend up in the same direction. But, when we get a reversal, the prediction continues upward for 5 bars after the reversal. That is, the prediction fails just when you need it the most. An interesting phenomenon is that, regardless of how far the extrapolation extends into the future, the prediction will always cross the signal at the same spot along the time axis. The result is that the prediction will have an overshoot. The amplitude of the overshoot is a function of how far the extrapolation has been carried into the future.
But the overshoot gives us an opportunity to make a useful prediction at the cyclic turning point of band limited signals (i.e. oscillators having a zero mean). If we reduce the overshoot by reducing the gain of the prediction, we then also move the crossing of the prediction and the original signal into the future. Since the group delay varies across the spectrum, the effect will be less effective for the shorter cycles in the data. Nonetheless, the technique is effective for both discretionary trading and automated trading in the majority of cases.
EXPLORING THE CODE
Before we predict, we need to create a band limited indicator from which to make the prediction. I have selected a “roofing filter” consisting of a High Pass Filter followed by a Low Pass Filter. The tunable parameter of the High Pass Filter is HPPeriod. Think of it as a “stone wall filter” where cycle period components longer than HPPeriod are completely rejected and cycle period components shorter than HPPeriod are passed without attenuation. If HPPeriod is set to be a large number (e.g. 250) the indicator will tend to look more like a trending indicator. If HPPeriod is set to be a smaller number (e.g. 20) the indicator will look more like a cycling indicator. The Low Pass Filter is a Hann Windowed FIR filter whose tunable parameter is LPPeriod. Think of it as a “stone wall filter” where cycle period components shorter than LPPeriod are completely rejected and cycle period components longer than LPPeriod are passed without attenuation. The purpose of the Low Pass filter is to smooth the signal. Thus, the combination of these two filters forms a “roofing filter”, named Filt, that passes spectrum components between LPPeriod and HPPeriod.
Since working into the future is not allowed in EasyLanguage variables, we need to convert the Filt variable to the data array XX . The data array is first filled with real data out to “Length”. I selected Length = 10 simply to have a convenient starting point for the prediction. The next block of code is the prediction into the future. It is easiest to understand if we consider the case where count = 0. Then, in English, the next value of the data array is equal to the current value of the data array plus the difference between the current value and the previous value. That makes the prediction one bar into the future. The process is repeated for each value of count until predictions up to 10 bars in the future are contained in the data array. Next, the selected prediction is converted from the data array to the variable “Prediction”. Filt is plotted in Red and Prediction is plotted in yellow.
The Predict Extrapolation indicator is shown above for the Emini S&P Futures contract using the default input parameters. Filt is plotted in red and Predict is plotted in yellow. The crossings of the Predict and Filt lines provide reliable buy and sell timing signals. There is some overshoot for the shorter cycle periods, for example in February and March 2021, but the only effect is a late timing signal. Further reducing the gain and/or reducing the BarsFwd inputs would provide better timing signals during this period.
ADDITIONS
Loxx's Expanded source types:
Library for expanded source types:
Explanation for expanded source types:
Three different signal types: 1) Prediction/Filter crosses; 2) Prediction middle crosses; and, 3) Filter middle crosses.
Bar coloring to color trend.
Signals, both Long and Short.
Alerts, both Long and Short.
Jurik-Filtered Kase Permission Stochastic [Loxx]Jurik-Filtered Kase Permission Stochastic is a special implementation of Kase Permission Stochastic by Kase StatWare. This implementation uses a Jurik filter to smooth final output.
What is Kase StatWare?
Kase StatWare has been around since 1992 and is a technical analysis trading indicator package developed by the acclaimed market technician and former energy trader Cynthia A. Kase. StatWare’s self-optimizing indicators help professional and individual traders to form a precise and systematic approach to discretionary trading and trade risk management.
Kase StatWare creates subscription-based technical analysis tools mainly for Stocks and Futures trading which can be subscribed to at a monthly cost.
What is Kase Permission Stochastic?
The Kase Permission Stochastic is a momentum indicator that examines a synthetic longer bar length, that by default, is three (5x by default for this implementation here) times higher than the bar length it is plotted against.
Included
Alerts
Signals
Bar coloring
OMA-Filtered Kase Permission Stochastic [Loxx]OMA-Filtered Kase Permission Stochastic is a special implementation of Kase Permission Stochastic by Kase StatWare.
What is Kase StatWare?
Kase StatWare has been around since 1992 and is a technical analysis trading indicator package developed by the acclaimed market technician and former energy trader Cynthia A. Kase. StatWare’s self-optimizing indicators help professional and individual traders to form a precise and systematic approach to discretionary trading and trade risk management.
Kase StatWare creates subscription-based technical analysis tools mainly for Stocks and Futures trading which can be subscribed to at a monthly cost.
What is Kase Permission Stochastic?
The Kase Permission Stochastic is a momentum indicator that examines a synthetic longer bar length, that by default, is three (5x by default for this implementation here) times higher than the bar length it is plotted against.
Included
Alerts
Signals
Bar coloring
