Black_Scholes: Black-Scholes formula and the Greeks

In qrmtools: Tools for Quantitative Risk Management

Black–Scholes formula and the Greeks

Description

Compute the Black–Scholes formula and the Greeks.

Usage

Black_Scholes(t, S, r, sigma, K, T, type = c("call", "put"))
Black_Scholes_Greeks(t, S, r, sigma, K, T, type = c("call", "put"))

Arguments

t	initial or current time t (in years).
S	stock price at time t.
r	risk-free annual interest rate.
sigma	annual volatility (standard deviation).
K	strike.
T	maturity (in years).
type	character string indicating whether a call (the default) or a put option is considered.

Details

Note again that t is time in years. In the context of McNeil et al. (2015, Chapter 9), this is \tau_t = t/250.

Value

Black_Scholes() returns the value of a European-style call or put option (depending on the chosen type) on a non-dividend paying stock.

Black_Scholes_Greeks() returns the first-order derivatives delta, theta, rho, vega and the second-order derivatives gamma, vanna and vomma (depending on the chosen type) in this order.

Author(s)

Marius Hofert

References

McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.

qrmtools documentation built on March 19, 2024, 3:08 a.m.