Suppose the greeks of the value of a derivative security are defined by (a) Find the relation

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Suppose the greeks of the value of a derivative security are defined by 

af at af as' = a2 f a S2

(a) Find the relation between Θ and Γ for a delta-neutral portfolio where Δ = 0. 

(b) Show that the theta may become positive for an in-the-money European call option on a continuous dividend paying asset when the dividend yield is sufficiently high. 

(c) Explain by financial argument why the theta value tends asymptotically to −rXe−rτ from below when the asset value is sufficiently high.

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