The Greeks
This application calculates the Greeks for a European call or put option using the Black-Scholes model.
Details on The Greeks
In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as time-value decay and the implied volatility or price of the underlying asset.
Delta - The price sensitivity
Delta measures the rate of change of the derivative value, V, with respect to changes in the underlying asset's price, S.
Δ=∂∂ S⁢V
Vega - The sensitivity to volatility
Vega measures the rate of change of the derivative value, V, with respect to the volatility, σ, of the underlying asset.
ν=∂∂ σ⁢V
Theta - The time sensitivity
Theta measures the rate of change of the derivative value, V, and time, τ. This is also known as the "time-value decay".
Θ=∂∂ τ⁢V
Rho - The sensitivity to the interest rate
Rho measures the rate of change of the derivative value, V, and the risk free interest rate, r.
ρ=∂∂ r⁢V
Gamma - The second-order time price sensitivity
Gamma measures the rate of change of the delta of a derivative, Δ, with respect to changes in the underlying asset's price, S.
Γ=∂∂ S⁢Δ=∂2∂ S2⁢V
Option Type
Parameters
Stock price
So =
Strike price
K =
Risk-free interest rate
r =
Dividend rate
q =
Time to maturity
T =
Volatility
σ =
Option Price
Delta
Δ =
Vega
ν=
Theta
Θ =
Rho
ρ =
Gamma
Γ =
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