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)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 the price
of a call (the default) or of put option is to be computed.
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).
McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.