GBSOption {RTL}

Generalized Black-Scholes (GBS) Option Pricing Model

Description

Computes the price and Greeks of European call and put options using the Generalized Black-Scholes model.

Usage

GBSOption(S, X, T2M, r, b, sigma, type = "call")

Arguments

S

numeric, the current stock price (also known as the underlying asset price).

X

numeric, the strike price of the option.

T2M

numeric, the time to maturity (in years). Previously denoted as T.

r

numeric, the risk-free interest rate (annualized).

b

numeric, the cost of carry, b = r - q for dividend paying assets, where q is the dividend yield rate.

sigma

numeric, the volatility of the underlying asset (annualized).

type

character, the type of option to evaluate, either "call" or "put". Default is "call".

Value

A list containing the following elements:

• price: The price of the option.

• delta: The sensitivity of the option's price to a change in the price of the underlying asset.

• gamma: The rate of change in the delta with respect to changes in the underlying price.

• vega: The sensitivity of the option's price to the volatility of the underlying asset.

• theta: The sensitivity of the option's price to the passage of time.

• rho: The sensitivity of the option's price to the interest rate.

Examples

GBSOption(S = 100, X = 100, T2M = 1, r = 0.05, b = 0.02, sigma = 0.2, type = "call")