\documentclass[a4paper,12pt]{article}

\begin{document}

\parindent=0pt

QUESTION

A pension fund manager expects to receive an inflow of funds in 60
days time. The manager would like to use these funds to buy a
stock that is currently trading at \$25 per share. The manager is
concerned that the stock price may rise and is only prepared to
pay a maximum of \$30 per share. A financial institution offers
him the following contract:

In 60 days' time, if the stock price is above \$30, the
institution will pay the fund the difference between the spot
price and \$30. If the stock price is below \$22, the fund manager
will pay the institution the difference between \$22 and the spot
price. What are the options involved, and justify your answer.


ANSWER

Payoff for pension fund (manager) is:

\setlength{\unitlength}{.5in}

\begin{picture}(7,7)

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

\put(0,3){\vector(1,0){7}}

\put(0,6){Payoff}

\put(.7,2.8){0}

\put(.7,1){22}

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

\put(3,3.1){22}

\put(5,2.8){30}

\put(5,3){\line(1,1){2}}

\put(7,3){$S$}

\put(4,2.9){0}

\put(1.8,1.8){$22-S$}

\put(5.8,3.8){$S-30$}

\end{picture}

Thus a solution is that fund is long one call with strike of 30
and short a put with strike price 22.

Payoff is:
$\max(S-30,0)-\max(22-S,0)=\left\{\begin{array}{cc}S-30,&S>30\\0&30>S>22\\22-S&22>S\end{array}\right.$




\end{document}
