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.

Δ= SV

 

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= σV

 

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= τV

 

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= rV

 

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= SΔ=2 S2V

 

Option Type

Parameters

Stock price

So = 

Strike price

K = 

Risk-free interest rate

r = 

Dividend rate

q = 

Time to maturity

T = 

Volatility

σ = 

The Greeks

Option Price

Delta

Δ = 

Vega

ν= 

Theta

Θ = 

Rho

ρ = 

Gamma

Γ = 

 

 


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