The Greeks - Maple Programming Help

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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, $S$. 

 Vega - The sensitivity to volatility Vega measures the rate of change of the derivative value, $V$, with respect to the volatility, $\mathrm{σ}$, of the underlying asset.

 Theta - The time sensitivity Theta measures the rate of change of the derivative value, $V$, and time, $\mathrm{τ}$. This is also known as the "time-value decay".

 Rho - The sensitivity to the interest rate Rho measures the rate of change of the derivative value, $V$, and the risk free interest rate, $r$.

 Gamma - The second-order time price sensitivity Gamma measures the rate of change of the delta of a derivative, $\mathrm{Δ}$, with respect to changes in the underlying asset's price, $S$.

 Option Type

 Parameters Stock price Strike price Risk-free interest rate Dividend rate Time to maturity Volatility

 The Greeks Option Price Delta Vega Theta Rho Gamma