<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}

\begin{document}

\parindent=0pt

QUESTION

Let the initial premium for an unhedged European option be $c$,
the strike price be $K$ and the asset price $S(T)$. Sketch the
actual payoff diagram as a function of $S$, including the initial
premium for:

\begin{description}

\item[(a)]
the holder of a call option,

\item[(b)]
the issuer of a call option,

\item[(c)]
the holder of a put option,

\item[(d)]
the issuer of a put option.

\end{description}
In each case identify the actual break even point relative to $K$.


ANSWER

\begin{description}

\item[(a)]
Exercise price is still $k$. Euro-call holder premium shifts
payoff down by premium $c$, so actual breakeven is $k+c$ for
holder.

\setlength{\unitlength}{0.5in}

\begin{picture}(7,5)

\put(0,2){\vector(1,0){6}}

\put(1,0){\vector(0,1){5}}

\put(0,4.8){payoff}

\put(4,2.1){$k$}

\put(4,2){\circle*{.1}}

\put(0.8,2.05){0}

\put(6,2){$S(T)$}

\put(.5,1.5){$c$}

\put(.8,1.2){\vector(0,1){0.8}}

\put(.8,2){\vector(0,-1){0.8}}

\put(1,1.2){\line(1,0){3}}

\put(4,1.2){\line(1,1){2}}

\put(4.8,1.8){$k+c$}

\put(4.8,2){\circle*{.1}}

\end{picture}

\item[(b)]

Euro-call issuer premium shifts payoff up by premium $c$. Note
that price at which holder will exercise still agrees for both
parties.

\setlength{\unitlength}{0.5in}

\begin{picture}(7,6)

\put(0,2){\vector(1,0){6}}

\put(1,0){\vector(0,1){6}}

\put(0,5.8){payoff}

\put(4,2.1){$k$}

\put(4,2){\circle*{.1}}

\put(0.8,1.7){0}

\put(6,2){$S(T)$}

\put(.5,2.5){$c$}

\put(.8,2){\vector(0,1){0.8}}

\put(.8,2.8){\vector(0,-1){0.8}}

\put(1,2.8){\line(1,0){3}}

\put(4,2.8){\line(1,-1){2}}

\put(4.8,1.8){$k+c$}

\put(4.8,2){\circle*{.1}}

\end{picture}

\item[(c)]
Euro-put holder premium shifts payoff down by amount $c$ so actual
breakeven is $k-c$ for holder.

\setlength{\unitlength}{0.5in}

\begin{picture}(7,7)

\put(0,2){\vector(1,0){6}}

\put(1,0){\vector(0,1){6}}

\put(0,4.8){payoff}

\put(4,2.1){$k$}

\put(4,2){\circle*{.1}}

\put(0.8,2.05){0}

\put(6,2){$S(T)$}

\put(5.5,1.5){$c$}

\put(5.8,1.2){\vector(0,1){0.8}}

\put(5.8,2){\vector(0,-1){0.8}}

\put(4,1.2){\line(1,0){2}}

\put(1,4.2){\line(1,-1){3}}

\put(1.2,5){$k$}

\put(1,5){\circle*{.1}}

\put(1.2,4.2){$k-c$}

\put(1,4.2){\circle*{.1}}

\put(3.2,2.1){$k-c$}

\put(3.2,2){\circle*{.1}}

\end{picture}

\item[(d)]
Euro-put issuer premium shifts payoff up by amount $c$. Exercise
price still the same for both parties.

\setlength{\unitlength}{0.5in}

\begin{picture}(7,7)

\put(0,3){\vector(1,0){6}}

\put(1,0){\vector(0,1){6}}

\put(0,4.8){payoff}

\put(4,3.1){$k$}

\put(4,3){\circle*{.1}}

\put(0.8,3.05){0}

\put(6,3){$S(T)$}

\put(5.5,3.3){$c$}

\put(5.8,3){\vector(0,1){0.8}}

\put(5.8,3.8){\vector(0,-1){0.8}}

\put(4,3.8){\line(1,0){2}}

\put(1,.8){\line(1,1){3}}

\put(1.2,0){$-k$}

\put(1,0){\circle*{.1}}

\put(1.2,.8){$-k+c$}

\put(1,.8){\circle*{.1}}

\put(3.2,2.7){$k-c$}

\put(3.2,3){\circle*{.1}}

\end{picture}

\end{description}




\end{document}
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