Added first section of option handout

Advanced/Options in Finance/parts/0 intro.tex

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+\section{Introduction}
+
+
+\vfill
+\pagebreak

Advanced/Options in Finance/parts/1 call.tex

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+\section{Call Options}
+
+\definition{}
+A \textit{call option} is an agreement between a buyer (B) and a seller (S): \par
+
+\begin{contract}[frametitle={Contract: Call Option}]
+	B pays S a premium $p$. \par
+	In return, S agrees to sell B a certain commodity $\mathbb{X}$ for a fixed price $k$ at a future time $t$.
+\end{contract}
+
+
+
+
+\problem{}<firstcall>
+B has ten call options for $\mathbb{X}$ at $23\Rub$. The current price of $\mathbb{X}$ is $20\Rub$. \par
+How much profit can B make if these contracts expire when $\mathbb{X}$ is $30\Rub$? \par
+\hint{When the contract expires, B can buy 10 shares of $\mathbb{X}$ at the price the contract set.}
+
+\begin{solution}
+	B has the right to buy 10 shares of $\mathbb{X}$ at $23\Rub$. \par
+	If B immediately sells them, his profit is $-230 + 300 = 70\Rub$
+\end{solution}
+
+
+\vfill
+
+
+
+\problem{}
+If B paid $10\Rub$ for the call options in \ref{firstcall}, how much money did he really make?
+
+\begin{solution}
+	$-10 + (-230 + 300) = 60\Rub$
+\end{solution}
+
+
+\vfill
+
+
+
+
+\problem{}
+Now, suppose that B bought and sold $\mathbb{X}$ directly instead of using a call option. \par
+How much profit would B have made?
+
+\begin{solution}
+	Buy for $200\Rub$, sell for $300\Rub$.\par
+	$-200 + 300 = 100\Rub$
+\end{solution}
+
+
+
+\vfill
+
+Given the results of the previous problems, why would anybody buy a call option?
+\pagebreak
+
+
+\problem{}
+Suppose $\mathbb{X}$ is worth $x_0$ right now. \par
+Call options to buy $\mathbb{X}$ at $k$ are sold for $p$.
+
+\begin{itemize}
+	\item What is the set of B's possible profit if..
+	\begin{itemize}
+		\item B buys a call option?
+		\item B buys $\mathbb{X}$ directly?
+	\end{itemize}
+	\hint{That is, what amounts of money can he make (or lose)?}
+
+	\item Are call options priced above or below the price of their stock? Why?
+	\item Why would anybody buy a call option?
+
+\end{itemize}
+
+
+\begin{solution}
+	\textbf{Call Option:} $[p, \infty)$ \par
+	If the price of $\mathbb{X}$ rises, there is no limit to how much money B can make. \par
+	If the price falls, $B$ can choose to let his contract expire, losing only $p$.
+
+	\vspace{2mm}
+
+	\textbf{Direct:} $[x_0, \infty)$\par
+	If the price of $\mathbb{X}$ rises, there is again no limit to how much money B can make. \par
+	If the price falls, $B$ will lose everything he paid for his shares of $\mathbb{X}$.
+
+	\vspace{2mm}
+
+	Of course, call options are priced below their stock. There wouldn't be a reason to buy then
+	if they were priced above!
+\end{solution}
+
+
+\vfill
+
+\problem{}
+Suppose $\mathbb{X}$ is worth $x_0$ right now. \par
+Call options to buy $\mathbb{X}$ at $k$ are sold for $p$. \par
+
+\vspace{2mm}
+Assume that S owns no stock---if B executes his contracts, she will buy stock and re-sell it to him. \par
+What are S's possible profits if she sells B a call option?
+
+\begin{solution}
+	$(-\infty, ~p]$
+
+	If the price of $\mathbb{X}$ rises, S will have to re-sell shares to B at a loss. \par
+	If the price falls, B could choose to buy shares from S at a loss, but he won't. \par
+	In this case, S only keeps the premium B paid for the contract.
+\end{solution}
+
+
+\vfill
+
+\pagebreak