Added finance sections

Advanced/Options in Finance/main.tex

@@ -86,5 +86,7 @@
 
 	\input{parts/0 intro}
 	\input{parts/1 call}
+	\input{parts/2 put}
+	\input{parts/3 compound}
 
 \end{document}

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

@@ -1,5 +1,19 @@
 \section{Introduction}
 
+\definition{}
+An \textit{asset} is any resource that has economic value.\par
+Examples: gold, oil, grain, cash, real estate, treasury bonds, etc
+
+\definition{}
+A \textit{stock} is a particular type of asset.
+A share of stock represents \say{partial ownership} of a corporation.
+Like many assets, stocks are \textit{intangible}---they only exist on paper.
+
+\problem{}
+Let $\mathbb{X}$ be a stock, currently priced at $19\Rub$. \par
+Bogdan buys 10 shares of $\mathbb{X}$, and sells them after a month for $23\Rub$ per share. \par
+What was his net profit?
+
 
 \vfill
 \pagebreak

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

@@ -5,7 +5,7 @@ A \textit{call option} is an agreement between a buyer (B) and a seller (S): \pa
 
 \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 $t$.
+	In return, S agrees to sell B a certain stock $\mathbb{X}$ for a fixed \say{strike price} $k$ at a future time $t$.
 \end{contract}
 
 
@@ -13,7 +13,7 @@ A \textit{call option} is an agreement between a buyer (B) and a seller (S): \pa
 
 \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
+How much profit can B make if these contracts expire when $\mathbb{X}$ is worth $30\Rub$? \par
 \hint{When the contract expires, B can buy 10 shares of $\mathbb{X}$ at the price the contract set.}
 
 \begin{solution}
@@ -51,14 +51,12 @@ How much profit would B have made?
 
 
 \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 $p$.
+Call options to buy $\mathbb{X}$ at strike price $k$ are sold for $p$.
 
 \begin{itemize}
 	\item What is the set of B's possible profit if..
@@ -66,10 +64,13 @@ Call options to buy $\mathbb{X}$ at $k$ are sold for $p$.
 		\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)?}
+	\hint{That is, what amounts of money can B 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?
+	\item On the previous page, we saw that the profit
+	made on a call option was much lower than the profit
+	made by buying a stock directly.
+	Why would anybody buy a call option?
 
 \end{itemize}
 
@@ -96,21 +97,79 @@ Call options to buy $\mathbb{X}$ at $k$ are sold for $p$.
 
 \problem{}
 Suppose $\mathbb{X}$ is worth $x_0$ right now. \par
-Call options to buy $\mathbb{X}$ at $k$ are sold for $p$. \par
+Call options to buy $\mathbb{X}$ for $k$ 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
+Assume that S owns no stock---if B executes his contracts, she will buy stock and resell it to him. \par
 What are S's possible profits if she sells B a call option?
 
 \begin{solution}
-	$(-\infty, ~p]$
+	$(-\infty, ~p]$\par
-
+	If the price of $\mathbb{X}$ rises, S will have to resell shares to B at a loss.
-	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.
-	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
+
+\problem{}
+How does the price of $\mathbb{X}$ at $t$ relate to the amount of
+profit B and S make? Complete the plots below.
+
+\null\hfill
+\begin{minipage}{0.48\textwidth}
+	\begin{center}
+		\begin{tikzpicture}
+			\draw (0,0) -- (5, 0);
+			\draw (0,-2) -- (0, 2);
+
+			\node at (2.5, 2) {Profit plot for $B$};
+
+
+			\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 (3, 0) {$k$};
+			\filldraw (3, 0) circle (0.5mm);
+		\end{tikzpicture}
+	\end{center}
+\end{minipage}
+\hfill
+\begin{minipage}{0.48\textwidth}
+	\begin{center}
+		\begin{tikzpicture}
+			\draw (0,0) -- (5, 0);
+			\draw (0,-2) -- (0, 2);
+
+			\node at (2.5, 2) {Profit plot for $S$};
+
+			\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 (3, 0) {$k$};
+			\filldraw (3, 0) circle (0.5mm);
+		\end{tikzpicture}
+	\end{center}
+\end{minipage}
+\hfill\null
+
+When does B make a positive profit? When does S? \par
+Write an equation that calculates S and B's earnings given
+$p$, $k$, and the price of $\mathbb{X}$ at the time the contract expires.
+
 
 \vfill
-
 \pagebreak

Advanced/Options in Finance/parts/2 put.tex

@@ -0,0 +1,55 @@
+\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
+

Advanced/Options in Finance/parts/3 compound.tex

@@ -0,0 +1,76 @@
+\section{Compound Strategies}
+
+\definition{}
+A \textit{covered call} is a trading strategy where one simultaneously
+buys a share of stock and sells a call option. When the contract
+expires, the stock is sold to the call buyer (if they choose
+to exercise their contract) or to the market (if they don't).
+
+\problem{}
+Say we set up a covered call by buying a share of $\mathbb{X}$ for $x_0$
+and selling a call option for $\mathbb{X}$ at $k$ for $p$. \par
+When our contract expires, $\mathbb{X}$
+is worth $x_1$.
+
+\vspace{2mm}
+
+What is the gross profit of a covered call?\par
+What is its net profit?\par
+\hint{Gross profit does not take setup cost into account. Net profit does.}
+
+
+\vfill
+
+\definition{}
+We say that trading strategy $A$ \textit{simulates} trading strategy
+$B$ if their net profits are equal.
+
+\problem{}
+Find a trading strategy that buys stock and call options
+to simulate a single put option with strike price $k$.
+
+\vfill
+
+
+\problem{}
+A \textit{straddle} is a trading strategy where one buys a call and a put
+with the same strike price and expiration. Plot the profit curve. \par
+What do you bet on when you buy a straddle?
+
+\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 (5, 0) {$k$};
+		\filldraw (5, 0) circle (0.5mm);
+	\end{tikzpicture}
+\end{center}
+
+\vfill
+\pagebreak
+
+\definition{}
+A \textit{butterfly spread} is a trading strategy where one buys two
+calls with strike prices $k_1$ and $k_2$ and sells two calls with strike
+prices $\frac{k_1+k_2}{2}$.
+
+\problem{}
+When should you set up a butterfly spread? \par
+Find the payoff function.
+
+\vfill
+
+
+\vfill
+\pagebreak
+