Consider an option with α being a non-negative parameter and the option pays ((S(T))α − K)+ at maturity date T. Let Cα(S

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Consider an option with α being a non-negative parameter and the
option
pays ((S(T))α − K)+ at maturity date T. Let Cα(S(0), σ, r) be the
risk neutral
price of the option (with interest rate r and volatility σ) when
the initial price is
S(0).
Obviously, C1(S(0), σ, r) = C(S(0), σ, r) is the price of an
ordinary call option.
Show that,
Cα(S(0), σ, r) = e(α−1)(r+ασ2/2)TC((S(0))α, ασ, rα),
where rα = α(r − σ2/2) + α2σ2/2.