Compute the Black--Scholes formula and the Greeks.
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"))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.
initial or current time \(t\) (in years).
stock price at time \(t\).
risk-free annual interest rate.
annual volatility (standard deviation).
strike.
maturity (in years).
character string indicating whether
a call (the default) or a put option is considered.
Marius Hofert
Note again that t is time in years. In the context of McNeil et
al. (2015, Chapter 9), this is \(\tau_t = t/250\).
McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.