\section{Put Options}

\definition{}
A \textit{put option} is an agreement between a buyer (B) and a seller (S): \par

\begin{contract}[frametitle={Contract: Put Option}]
	B pays S a premium $p$. \par
	In return, S agrees to buy a certain stock $\mathbb{X}$ from S for a fixed \say{strike price} $k$ at a future time $t$,
	if B decides to exercise this contract.
\end{contract}

As before, the \textbf{buyer} decides whether or not this contract is put into action. \par
Also, note that B does not need to own any shares of stock to buy a put option. \par
He may buy them whenever he wishes.

\problem{}
How is a put different from a call? \par
What is S betting on? What is B betting on?

\vfill

\problem{}
Suppose B paid $100\Rub$ for 300 put contracts on $\mathbb{X}$ at $17\Rub$.\par
At time the contracts expired, the price of $\mathbb{X}$ was $20\Rub$.\par
What is B's profit?

\vfill

\problem{}
Plot profit curves for selling a put option, buying a put option,
and buying a stock directly on the axis below.

\begin{center}
	\begin{tikzpicture}
		\draw (0,0) -- (10, 0);
		\draw (0,-3) -- (0, 3);


		\node[
			anchor = south,
			rotate = 90
		] at (0,0) {\color{gray}Profit};

		\node[
			anchor = south west,
		] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$};

		\node[anchor = north] at (6, 0) {$k$};
		\filldraw (6, 0) circle (0.5mm);
	\end{tikzpicture}
\end{center}

\vfill
\pagebreak