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QUESTION

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

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

Continuously compounded annual risk-free rate 5.60\%;

Volatility 20\%; current price \$50

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


ANSWER

$k=60$ (different from question 6), $r=0.056,\ \sigma=0.2,\
s_0=50,\ U=1.17283,\ D=0.88389$

\underline{Europut} Summary:

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\begin{picture}(10,10)

\put(0,5.5){$P_0=8.807637$} \put(0,5){$\phi_0=-0.70456$}
\put(0,4.5){$\psi_0=44.03553$} \put(0,4){$S_0=50$}

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

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

\put(5,3.5){$P_1^-=14.14856$} \put(5,3){$\phi_1^-=-1$}
\put(5,2.5){$\psi_1^-=58.34306$} \put(5,2){$S_1^-=44.1945$}

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

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

\put(5,7.5){$P_1^+=3.969809$} \put(5,7){$\phi_1^+=-0.48202$}
\put(5,6.5){$\psi_1^+=32.23645$} \put(5,6){$S_1^+=658.6415$}

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

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

\put(8,1){$P_2^-=20.93692$} \put(8,.5){$S_2^-=39.06308$}

\put(8,5){$P_2^0=8.167365$} \put(8,4.5){$S_2^0=51.83264$}

\put(8,9.5){$P_2^+=0$} \put(8,9){$\phi_2^+=0$}
\put(8,8.5){$\psi_2^+=0$} \put(8,8){$S_2^+=68.77651$}

\end{picture}

Put premium $P_0$ increases as $k$ increases (opposite of call).




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