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Greeks

Greeks - v t,x 0 2K t T 0 x Black-Scholes price of a...

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0 T t 0 2K x v t,x Black-Scholes price of a European call ( S T K ) + as a function of time t [0 , T ] and spot S t = x [0 , 2 K ]. 1

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0 T t 0 2K x 1 t,x The option’s Delta, ( t, x ) = x v ( t, x ) = N ° d + ¢ 2
0 T t 0 2K x t,x The option’s Gamma, Γ ( t, x ) = x ( t, x ) = 2 x 2 v ( t, x ) = N 0 ° d + ¢ x σ T t . 3

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0 T t 0 2K x t,x The option’s Theta, Θ ( t, x ) = t v ( t, x ) = x σ 2 T t N 0 ° d + ¢ Kr e r ( T t ) N ° d ¢ . 4
0 T t 0 2K x Ρ t,x The option’s Rho, % ( x, t ) = r v ( x, t ) = K ( T t ) e r ( T t ) N ° d ¢ . 5

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0 T t 0 2K x Vega t,x The option’s Vega, V ( x, t ) = ∂σ v ( x, t ) = x T t N 0 °
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