greeks: Sensitivities of Prices of Financial Options and Implied Volatilities

Abstract

Summary The greeks R package leverages the Black-Scholes model and more general jump diffusion models to compute sensitivities of financial option prices for European, geometric and arithmetic Asian, as well as American options, with various payoff functions (for a treatment see Hull (2022), and Angus (1999) for the case of geometric Asian options). The Black-Scholes model is the standard approach for modelling stock prices, while jump diffusion models aim to offer a more realistic representation of market movements, see Kou (2002). Furthermore, methods to compute implied volatilities are provided for a wide range of option types and custom payoff functions. Classical formulas are implemented for European options in the Black-Scholes model, as is presented in Hull (2022). In the case of Asian options, Malliavin Monte Carlo Greeks are implemented, see Hudde & Rüschendorf (2023), or Lyuu et al. (2019). For American options, the Binomial Tree method is implemented, as is presented in Hull (2022). greeks includes a Shiny app to interactively plot the results.