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Considere una opcin de llamada de poder. Esta opcin tiene un parmetro adicional, ( alpha>0 ). La opcin paga la cantidad ( S_{T}^{alpha} ) si

Considere una opcin de llamada de poder. Esta opcin tiene un parmetro adicional, \( \alpha>0 \). La opcin paga la cantidad \( S_{T}^{\alpha} \) si se ejerce en la fecha de vencimiento \( T \). busque el precio de la opcin dado por \[ \exp \left[(\alpha-1)\left(r+\frac{1}{2} \sigma^{2} ight) T+\alpha^{2} \ sigma^{2} T / 2 ight] S_{0}^{\alpha} \Phi\left(\tilde{d}{1} ight)-e^{-r T} K \Phi\left( \tilde{d}_{2} ight) \] donde \( \tilde{d}_{i}=\ln \left(e^{r T} S{0} / K^{1 / \alpha } ight) /(\sigma \sqrt{T}) \pm \alpha \sigma \sqrt{T} / 2, i=1,2 \). Sugerencia: El valor de la opcin esta dado por \( e^{r T} \mathbb{E}\left[\left(S_{T}^{\alpha}-K ight){+} ight] \ )evalue esta integral como en el caso de la call y use el hecho de que \[ S{T}^{\alpha}=S_{0}^{\alpha} e^{\left[\alpha\left(r -0,5 * \sigma^{2} ight) T+\alpha \sigma \sqrt{T} Z ight]} \] donde \( Z \) se distribuye como una \( N(0,1) \ ).

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