American Approximation Bjerksund & Stensland 1993 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 and Stensland (1993) approximation can be used to price American options on stocks,...
American Approximation: Barone-Adesi and Whaley 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.
An American option can be exercised at any time up to its expiration date. This added freedom...
Samuelson 1965 Option Pricing Formula is an options pricing formula that pre-dates Black-Scholes-Merton. This version includes Analytical Greeks.
Samuelson (1965; see also Smith, 1976) assumed the asset price follows a geometric Brownian motion with positive drift, p. In this way he allowed for positive interest rates and a risk premium.
c = SN(d1) * e^((rho...
Boness 1964 Option Pricing Formula is an options pricing model that pre-dates Black-Scholes-Merton. This model includes Analytical Greeks.
Boness (1964) assumed a lognormal asset price. Boness derives the following value for a call option:
c = SN(d1) - Xe^(rho * T)N(d2)
d1 = (log(S / X) + (rho + v^2 / 2) * T) / (v * T^0.5)
d2 = d1 - (v * T^0.5)
where rho...
Generalized Black-Scholes-Merton on Variance Form is an adaptation of the Black-Scholes-Merton Option Pricing Model including Numerical Greeks. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". This version is to price Options using variance instead of volatility.
Black- Scholes- Merton on Variance Form
In some...
Asay (1982) Margined Futures Option Pricing Model 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 is to price Options on Futures where premium is fully margined. This...
Black-76 Options on Futures 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 is to price Options on Futures. The options sensitivities (Greeks) are the partial derivatives...
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...
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 1973 OPM on Non-Dividend Paying Stocks is an adaptation of the Black-Scholes-Merton Option Pricing Model including Analytical Greeks and implied volatility calculations. Making b equal to r yields the BSM model where dividends are not considered. The following information is an excerpt from Espen Gaarder Haug's book "Option Pricing Formulas". The...
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...
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...
Sprenkle 1964 Option Pricing Model w/ Num. Greeks is an adaptation of the Sprenkle 1964 Option Pricing Model in Pine Script. The following information is an except from Espen Gaarder Haug's book "Option Pricing Formulas".
The Sprenkle Model
Sprenkle (1964) assumed the stock price was log-normally distributed and thus that the asset price followed a geometric...
Modified Bachelier Option Pricing Model w/ Num. Greeks is an adaptation of the Modified Bachelier Option Pricing Model in Pine Script. The following information is an except from Espen Gaarder Haug's book "Option Pricing Formulas".
Before Black Scholes Merton
The curious reader may be asking how people priced options before the BSM breakthrough was published...
Bachelier 1900 Option Pricing Model w/ Numerical Greeks is an adaptation of the Bachelier 1900 Option Pricing Model in Pine Script. The following information is an except from Espen Gaarder Haug's book "Option Pricing Formulas"
Before Black Scholes Merton
The curious reader may be asking how people priced options before the BSM breakthrough was published in...
The Black Scholes Merton model
If you are new to options I strongly advise you to profit from Robert Shiller's lecture on same . It combines practical market insights with a strong authoritative grasp of key models in option theory. He explains many of the areas covered below and in the following pages with a lot intuition and relatable anecdotage. We start here...
Boyle Trinomial Options Pricing Model is an options pricing indicator that builds an N-order trinomial tree to price American and European options. This is different form the Binomial model in that the Binomial assumes prices can only go up and down wheres the Trinomial model assumes prices can go up, down, or sideways (shoutout to the "crab" market enjoyers)....
Implied Volatility Estimator using Black Scholes derives a estimation of implied volatility using the Black Scholes options pricing model. The Bisection algorithm is used for our purposes here. This includes the ability to adjust for dividends.
Implied Volatility
The implied volatility (IV) of an option contract is that value of the volatility of the...
![WMT: American Approximation Bjerksund & Stensland 1993 [Loxx]](https://s3.tradingview.com/e/EGAr7TMG_mid.png "American Approximation Bjerksund & Stensland 1993 [Loxx]")
![WMT: American Approximation: Barone-Adesi and Whaley [Loxx]](https://s3.tradingview.com/2/2NDydZJQ_mid.png "American Approximation: Barone-Adesi and Whaley [Loxx]")
![WMT: Samuelson 1965 Option Pricing Formula [Loxx]](https://s3.tradingview.com/q/QHFCDFzu_mid.png "Samuelson 1965 Option Pricing Formula [Loxx]")
![WMT: Boness 1964 Option Pricing Formula [Loxx]](https://s3.tradingview.com/r/RjLacOHv_mid.png "Boness 1964 Option Pricing Formula [Loxx]")
![WMT: Generalized Black-Scholes-Merton on Variance Form [Loxx]](https://s3.tradingview.com/s/SHgHh05Y_mid.png "Generalized Black-Scholes-Merton on Variance Form [Loxx]")
![WMT: Asay (1982) Margined Futures Option Pricing Model [Loxx]](https://s3.tradingview.com/w/W362GSmU_mid.png "Asay (1982) Margined Futures Option Pricing Model [Loxx]")
![WMT: Black-76 Options on Futures [Loxx]](https://s3.tradingview.com/v/VpsGfVA5_mid.png "Black-76 Options on Futures [Loxx]")
![WMT: Garman and Kohlhagen (1983) for Currency Options [Loxx]](https://s3.tradingview.com/4/43KUMLqw_mid.png "Garman and Kohlhagen (1983) for Currency Options [Loxx]")
![WMT: BSM OPM 1973 w/ Continuous Dividend Yield [Loxx]](https://s3.tradingview.com/e/ecJOXGMw_mid.png "BSM OPM 1973 w/ Continuous Dividend Yield [Loxx]")
![WMT: Black-Scholes 1973 OPM on Non-Dividend Paying Stocks [Loxx]](https://s3.tradingview.com/f/FRZfgQ7U_mid.png "Black-Scholes 1973 OPM on Non-Dividend Paying Stocks [Loxx]")
![WMT: Generalized Black-Scholes-Merton w/ Analytical Greeks [Loxx]](https://s3.tradingview.com/f/foImvlF1_mid.png "Generalized Black-Scholes-Merton w/ Analytical Greeks [Loxx]")
![WMT: Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]](https://s3.tradingview.com/m/mKNkV192_mid.png "Generalized Black-Scholes-Merton Option Pricing Formula [Loxx]")
![WMT: Sprenkle 1964 Option Pricing Model w/ Num. Greeks [Loxx]](https://s3.tradingview.com/3/3ERjyUcZ_mid.png "Sprenkle 1964 Option Pricing Model w/ Num. Greeks [Loxx]")
![WMT: Modified Bachelier Option Pricing Model w/ Num. Greeks [Loxx]](https://s3.tradingview.com/k/KTT2ddmK_mid.png "Modified Bachelier Option Pricing Model w/ Num. Greeks [Loxx]")
![WMT: Bachelier 1900 Option Pricing Model w/ Numerical Greeks [Loxx]](https://s3.tradingview.com/n/NIVdMK6Y_mid.png "Bachelier 1900 Option Pricing Model w/ Numerical Greeks [Loxx]")
![SPY: Black Scholes Option Pricing Model w/ Greeks [Loxx]](https://s3.tradingview.com/w/WobQqSxF_mid.png "Black Scholes Option Pricing Model w/ Greeks [Loxx]")
![SPY: Boyle Trinomial Options Pricing Model [Loxx]](https://s3.tradingview.com/i/IgEbTjmh_mid.png "Boyle Trinomial Options Pricing Model [Loxx]")
![SPY: Implied Volatility Estimator using Black Scholes [Loxx]](https://s3.tradingview.com/x/xT4abuhx_mid.png "Implied Volatility Estimator using Black Scholes [Loxx]")