https://github.com/ahudde/greeks
Sensitivities of Prices of Financial Options and Implied Volatilites
https://github.com/ahudde/greeks
asian-option greeks implied-volatility option r-package
Last synced: 8 months ago
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Sensitivities of Prices of Financial Options and Implied Volatilites
- Host: GitHub
- URL: https://github.com/ahudde/greeks
- Owner: ahudde
- License: other
- Created: 2021-05-16T14:26:33.000Z (about 5 years ago)
- Default Branch: main
- Last Pushed: 2025-03-14T11:24:12.000Z (about 1 year ago)
- Last Synced: 2025-10-17T20:48:53.623Z (8 months ago)
- Topics: asian-option, greeks, implied-volatility, option, r-package
- Language: R
- Homepage:
- Size: 23.6 MB
- Stars: 7
- Watchers: 1
- Forks: 4
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- Changelog: NEWS.md
- License: LICENSE
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README
# `greeks`
[](https://github.com/ahudde/greeks/actions/workflows/R-CMD-check.yaml)
[](https://doi.org/10.21105/joss.05987)
[](https://app.codecov.io/gh/ahudde/greeks?branch=main)
The package `greeks` provides functions to compute financial option prices and
sensitivities of financial option prices for European, American, Asian, and
Digital options in the Black Scholes model, and in more general jump diffusion
models.
Furthermore, based on the implementations of Vega, efficient functions for
calculating implied volatilities not just for European options, but also for
American, Asian, and digital options are provided.
Classical formulas are implemented for European options in the Black Scholes
Model.
Furthermore, functions to calculate Malliavin Monte Carlo Greeks are given, as
presented e.g., in Hudde, A. & Rüschendorf, L. (2016).
European and Asian Greeks for exponential Lévy processes
(https://link.springer.com/article/10.1007/s11009-023-10014-5).
These functions work for classical payoff functions, as well as for any custom
square integrable function provided by the user.
Additionally, these calculations are not restricted to the Black Scholes model,
but work for more general Lévy Jump diffusion model, which is also customizable
by the user.
## `greeks` on CRAN
You can view the documentation of this package on
[CRAN.R-project.org/package=greeks/greeks.pdf](https://CRAN.R-project.org/package=greeks/greeks.pdf)
and the vignette on
[CRAN.R-project.org/package=greeks/vignettes/using_greeks.html](https://CRAN.R-project.org/package=greeks/vignettes/using_greeks.html).
## Installation
# The cran version can be installed by
install.packages("greeks")
# The development version can be installed by
install.packages("devtools")
library("devtools")
devtools::install_github("ahudde/greeks")
## Computing option prices and Greeks in the shiny app
The option prices and volatilities for European options can be displayed with
the interactive shiny app by calling
library(greeks)
Greeks_UI()
or online on
[anselmhudde.shinyapps.io/greeks/](https://anselmhudde.shinyapps.io/greeks/)
## The function `Greeks`
Most of the options prices and Greeks can easily be calculated with the function
Greeks.
# Load package
library(greeks)
# Option price and most common Greeks of a European call option on a share with
# price 100 and volatility of 30%, where the exercise price is 120, the time to
# maturity of 5 years, and the riskless interest rate of 1%.
Greeks(initial_price = 100,
exercise_price = 120,
r = 0.01,
time_to_maturity = 5,
volatility = 0.30,
payoff = "call")
## fair_value delta vega theta rho
## 21.577149923 0.554941778 88.358901748 -2.989937331 169.585139380
## gamma
## 0.005890593
# Option price and most common Greeks of an American put option on a share with
# price 100 and volatility of 25%, where the exercise price is 100, the time to
# maturity of 1 year, and the riskless interest rate of -0.5%.
Greeks(initial_price = 100,
exercise_price = 100,
r = -0.005,
time_to_maturity = 1,
volatility = 0.30,
payoff = "put",
option_type = "American")
## fair_value delta vega theta rho gamma
## 12.2027075 -0.4469782 39.5313017 -6.2141979 -56.9005269 -0.1275472
## Computing implied volatilities
The package `greeks` also provides a function to compute implied volatilities
for a wide range of option types and payoff functions:
# Implied volatility of an Asian call option with on an option price of 15, a
# share price of 100, an exercise_price of 100, a risk-free interest rate of
# 0.05 and a time to maturity of 1.
Implied_Volatility(option_price = 15, initial_price = 100,
exercise_price = 100, r = 0.05, time_to_maturity = 1,
option_type = "Asian", payoff = "call")
## [1] 0.6330451
## Contributions, bug reports or support
Bug reports and contributions are very welcome.
Also, if you need assistance, please open an issue on [github.com/ahudde/greeks/issues](https://github.com/ahudde/greeks/issues).