# greeks   The package `greeks` provides functions to compute financial option prices and sensitivities of financial option prices for European, Asian, American and Digital options in the Black Scholes model, and in more general jump diffusion models. Furthermore, based on the implementations of Vega, efficient funcions for calculting 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://arxiv.org/abs/1603.00920). 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.

## Installation

`{r } # 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("anselmhudde/greeks")`

## How to start

Most of the options prices and Greeks can easily can calculated with the function Greeks.

``````# Load package

library(greeks)

# Option price and most common Greeks of an 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 volatilies for a wide range of options types and payoff functions:

``````# Implied volatiliy 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")

##  0.6330451``````