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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:

\begin{center}

Strike \$60; Maturity 1 year, two intervals;

Continuously compounded annual risk-free rate 5\%;

Volatility 25\%; Current price \$50.

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What do you notice about the way the premium behaves with strike
price for a call option?


ANSWER

$k=\$60,\ r=0.05,\ \sigma=0.25,\ S_0=\$50,\ U=1.20460,\ D=0.84586$

\underline{Eurocall} Summary:

\setlength{\unitlength}{.5in}

\begin{picture}(10,10)

\put(0,5.5){$C_0=2.988178$} \put(0,5){$\phi_0=0.341451$}
\put(0,4.5){$\psi_0=-14.0844$} \put(0,4){$S_0=50$}

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

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

\put(5,3.5){$C_1^-=0$} \put(5,3){$\phi_1^-=0$}
\put(5,2.5){$\psi_1^-=0$} \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){$C_1^+=6.124603$} \put(5,7){$\phi_1^+=0.580974$}
\put(5,6.5){$\psi_1^+=-28.8675$} \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){$C_2^0=0$} \put(8,4.5){$S_2^0=50.94615$}

\put(8,9.5){$C_2^+=12.55306$} \put(8,9){$S_2^+=72.55306$}

\end{picture}

$C_0$ decreases with $k$ increasing.



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