qrmtools (version 0.0-4)

Black_Scholes: 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)

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 the price of a call (the default) or of put option is to be computed.

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 (in this order).

References

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