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QUESTION

Calculate the initial premium and the trading strategy for the
asset/bond replicating portfolio for a European call option on the
following data:

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Strike \$50; Maturity 1 year, two intervals;

Continuously compounded annual risk-free rate 5\%;

Volatility 25\%; Current price \$50.

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ANSWER

$\begin{array}{c}k=50\\r=0.05\end{array}$

$\left.\begin{array}{c}\sigma=0.25\\s_0=50\end{array}\right\}$
main changes from question 2.

$U=e^{\left[\left(0.05-\frac{0.25^2}{2}\right)\times\frac{1}{2}+
0.25\sqrt{\frac{1}{2}}\right]}=1.20460\\
D=e^{\left[\left(0.05-\frac{0.25^2}{2}\right)-0.25\sqrt{\frac{1}{2}}\right]}=0.84586$


\underline{Eurocall} Summary:

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\begin{picture}(10,10)

\put(0,5.5){$C_0=5.818613$} \put(0,5){$\phi_0=0.613431$}
\put(0,4.5){$\psi_0=-24.8529$} \put(0,4){$S_0=50$}

\put(2,5){\line(3,2){3}}

\put(2,5){\line(3,-2){3}}

\put(5,3.5){$C_1^-=0.461623$} \put(5,3){$\phi_1^-=0.062361$}
\put(5,2.5){$\psi_1^-=-2.1758$} \put(5,2){$S_1^-=42.293$}

\put(7,4){\line(1,1){1}}

\put(7,2){\line(1,-1){1}}

\put(5,7.5){$C_1^+=11.46474$} \put(5,7){$\phi_1^+=1$}
\put(5,6.5){$\psi_1^+=-48.7653$} \put(5,6){$S_1^+=60.23$}

\put(7,8){\line(1,1){1}}

\put(7,6){\line(1,-1){1}}

\put(8,1){$C_2^-=0$} \put(8,.5){$S_2^-=35.77396$}

\put(8,5){$C_2^0=0.946148$} \put(8,4.5){$S_2^0=50.94615$}

\put(8,9.5){$C_2^+=22.55306$} \put(8,9){$S_2^+=72.55306$}

\end{picture}




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